From 5ee82f1f106c61a8cfb96def7f6100daf6fd1630 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 27 Sep 2023 02:10:20 +0000 Subject: [PATCH] build based on a7cc3a3 --- dev/guide/guide.html | 2 +- dev/index.html | 2 +- dev/man/functions.html | 22 +++++++++++----------- dev/man/reference.html | 2 +- dev/man/types.html | 4 ++-- dev/search.html | 2 +- 6 files changed, 17 insertions(+), 17 deletions(-) diff --git a/dev/guide/guide.html b/dev/guide/guide.html index 4a74989..6a6f4b1 100644 --- a/dev/guide/guide.html +++ b/dev/guide/guide.html @@ -1,2 +1,2 @@ -How to guide · FinEtoolsFlexStructures.jl
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Guide

The FinEtoolsFlexStructures package is used to solve static and dynamic linear and nonlinear problems involving beams and linear static and dynamic analysis of shells.

The basic functionality is provided by the FinEtools package.

To understand how the package works, we would suggest inspecting the examples. The examples are organized by category: statics, dynamics, etc. There is usually an indication of what the correct answer should be (frequencies, deflections, buckling factors, ...). Many examples correspond to well-known benchmarks.

+How to guide · FinEtoolsFlexStructures.jl
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Guide

The FinEtoolsFlexStructures package is used to solve static and dynamic linear and nonlinear problems involving beams and linear static and dynamic analysis of shells.

The basic functionality is provided by the FinEtools package.

To understand how the package works, we would suggest inspecting the examples. The examples are organized by category: statics, dynamics, etc. There is usually an indication of what the correct answer should be (frequencies, deflections, buckling factors, ...). Many examples correspond to well-known benchmarks.

diff --git a/dev/index.html b/dev/index.html index 4c47cef..535265a 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -Home · FinEtoolsFlexStructures.jl
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FinEtoolsFlexStructures Documentation

<!–- ## Tutorials

The tutorials are provided in the form of Julia scripts and Markdown files in a separate package. –->

Manual

The description of the types and the functions, organized by module and/or other logical principle.

+Home · FinEtoolsFlexStructures.jl
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FinEtoolsFlexStructures Documentation

<!–- ## Tutorials

The tutorials are provided in the form of Julia scripts and Markdown files in a separate package. –->

Manual

The description of the types and the functions, organized by module and/or other logical principle.

diff --git a/dev/man/functions.html b/dev/man/functions.html index a644446..2465117 100644 --- a/dev/man/functions.html +++ b/dev/man/functions.html @@ -1,25 +1,25 @@ -Functions · FinEtoolsFlexStructures.jl
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Functions

Table of Contents

CrossSectionModule functions

CompositeLayupModule functions

FinEtoolsFlexStructures.CompositeLayupModule.cartesian_csys — Method
cartesian_csys(axes)

Create a material Cartesian coordinate system.

  • axes = tuple of signed labels of the axes. For instance, (1, 2, 3) creates a coordinate system identical to the global cartesian coordinate system. (2, 1, -3) creates a coordinate system so that the first material basis vector is along the second global basis vector, the second material basis vector is along the first global basis vector, and the third material basis vector is opposite to the third global basis vector.
source
FinEtoolsFlexStructures.CompositeLayupModule.laminate_stiffnesses! — Method
laminate_stiffnesses!(cl::CompositeLayup, A, B, C)

Compute the laminate stiffnesses, membrane, extension-bending coupling, and bending.

Aij coefficients represent in-plane stiffness of the laminate, the Cij coefficients represent bending stiffness, the Bij represent bending-extension coupling.

source
FinEtoolsFlexStructures.CompositeLayupModule.plane_stress_T_matrix! — Method
plane_stress_T_matrix!(Tm::Array{T, 2}, angle) where {T}

Compute the transformation matrix of stress vector components FROM the PLY coordinate system TO the LAYOUT coordinate system.

angle = angle (in radians) between the first basis vector of the layup coordinate system and the first basis vector of the ply coordinate system m, n = cosine and sine of the angle

The nomenclature is from Barbero, Finite element analysis of composite materials using Abaqus (2013).

source
FinEtoolsFlexStructures.CompositeLayupModule.plane_stress_Tbar_matrix! — Method
plane_stress_Tbar_matrix!(Tm::Array{T, 2}, angle) where {T}
-plane_stress_Tbar_matrix!(Tm::Array{T, 2}, m, n) where {T}

Compute the transformation matrix of engineering strain components FROM the LAYUP coordinate system TO the PLY coordinate system.

angle = angle (in radians) between the first basis vector of the layup coordinate system and the first basis vector of the ply coordinate system m, n = cosine and sine of the angle

The nomenclature is from Barbero, Finite element analysis of composite materials using Abaqus (2013).

source
FinEtoolsFlexStructures.CompositeLayupModule.plane_stress_Tinv_matrix! — Method
plane_stress_Tinv_matrix!(Tinvm::Array{T, 2}, angle) where {T}
-plane_stress_Tinv_matrix!(Tinvm::Array{T, 2}, m, n) where {T}

Compute the transformation matrix of the stress vector components FROM the LAYOUT coordinate system TO the PLY coordinate system.

angle = angle (in radians) between the first basis vector of the layup coordinate system and the first basis vector of the ply coordinate system m, n = cosine and sine of the angle

The nomenclature is from Barbero, Finite element analysis of composite materials using Abaqus (2013).

source
FinEtoolsFlexStructures.CompositeLayupModule.transverse_shear_T_matrix! — Method
transverse_shear_T_matrix!(Tm::Array{T, 2}, angle) where {T}
-transverse_shear_T_matrix!(Tm::Array{T, 2}, m, n) where {T}

Compute the transformation matrix for the transverse shear stresses FROM the LAYOUT coordinate system TO the PLY coordinate system.

angle = angle (in radians) between the first basis vector of the layup coordinate system and the first basis vector of the ply coordinate system m, n = cosine and sine of the angle

source

FESetShellT3Module functions

MeshFrameMemberModule functions

FEMMCorotBeamModule functions

FinEtoolsFlexStructures.FEMMCorotBeamModule.distribloads_global — Method
distribloads_global(self::FEMMCorotBeam, geom0::NodalField{FFlt}, u1::NodalField{T}, Rfield1::NodalField{T}, dchi::NodalField{T}, fi) where {T<:Number}

Compute the load vector due to distributed loads.

Compute the global load vector corresponding to applied distributed load. Here it means force per unit length of the beam, in the configuration u1, Rfield1. These are only forces, not moments.

Note

The force intensity must be uniform across the entire element. The force intensity is given in the global coordinates.

source
FinEtoolsFlexStructures.FEMMCorotBeamModule.gyroscopic — Method
gyroscopic(self::FEMMCorotBeam,  assembler::A,
+Functions · FinEtoolsFlexStructures.jl
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Functions
Table of Contents
CrossSectionModule functions
CompositeLayupModule functions
FinEtoolsFlexStructures.CompositeLayupModule.cartesian_csys — Method
cartesian_csys(axes)
Create a material Cartesian coordinate system.
  • axes = tuple of signed labels of the axes. For instance, (1, 2, 3) creates a coordinate system identical to the global cartesian coordinate system. (2, 1, -3) creates a coordinate system so that the first material basis vector is along the second global basis vector, the second material basis vector is along the first global basis vector, and the third material basis vector is opposite to the third global basis vector.
source
FinEtoolsFlexStructures.CompositeLayupModule.laminate_stiffnesses! — Method
laminate_stiffnesses!(cl::CompositeLayup, A, B, C)
Compute the laminate stiffnesses, membrane, extension-bending coupling, and bending.
Aij coefficients represent in-plane stiffness of the laminate, the Cij coefficients represent bending stiffness, the Bij represent bending-extension coupling.
source
FinEtoolsFlexStructures.CompositeLayupModule.plane_stress_T_matrix! — Method
plane_stress_T_matrix!(Tm::Array{T, 2}, angle) where {T}
Compute the transformation matrix of stress vector components FROM the PLY coordinate system TO the LAYOUT coordinate system.
angle = angle (in radians) between the first basis vector of the layup     coordinate system and the first basis vector of the ply coordinate system m, n = cosine and sine of the angle
The nomenclature is from Barbero, Finite element analysis of composite materials using Abaqus (2013).
source
FinEtoolsFlexStructures.CompositeLayupModule.plane_stress_Tbar_matrix! — Method
plane_stress_Tbar_matrix!(Tm::Array{T, 2}, angle) where {T}
+plane_stress_Tbar_matrix!(Tm::Array{T, 2}, m, n) where {T}
Compute the transformation matrix of engineering strain components FROM the LAYUP coordinate system TO the PLY coordinate system.
angle = angle (in radians) between the first basis vector of the layup     coordinate system and the first basis vector of the ply coordinate system m, n = cosine and sine of the angle
The nomenclature is from Barbero, Finite element analysis of composite materials using Abaqus (2013).
source
FinEtoolsFlexStructures.CompositeLayupModule.plane_stress_Tinv_matrix! — Method
plane_stress_Tinv_matrix!(Tinvm::Array{T, 2}, angle) where {T}
+plane_stress_Tinv_matrix!(Tinvm::Array{T, 2}, m, n) where {T}
Compute the transformation matrix of the stress vector components FROM the LAYOUT coordinate system TO the PLY coordinate system.
angle = angle (in radians) between the first basis vector of the layup     coordinate system and the first basis vector of the ply coordinate system m, n = cosine and sine of the angle
The nomenclature is from Barbero, Finite element analysis of composite materials using Abaqus (2013).
source
FinEtoolsFlexStructures.CompositeLayupModule.transverse_shear_T_matrix! — Method
transverse_shear_T_matrix!(Tm::Array{T, 2}, angle) where {T}
+transverse_shear_T_matrix!(Tm::Array{T, 2}, m, n) where {T}
Compute the transformation matrix for the transverse shear stresses  FROM the LAYOUT coordinate system TO the PLY coordinate system.
angle = angle (in radians) between the first basis vector of the layup     coordinate system and the first basis vector of the ply coordinate system m, n = cosine and sine of the angle
source
FESetShellT3Module functions
MeshFrameMemberModule functions
FEMMCorotBeamModule functions
FinEtoolsFlexStructures.FEMMCorotBeamModule.distribloads_global — Method
distribloads_global(self::FEMMCorotBeam, geom0::NodalField{FFlt}, u1::NodalField{T}, Rfield1::NodalField{T}, dchi::NodalField{T}, fi) where {T<:Number}
Compute the load vector due to distributed loads.
Compute the global load vector corresponding to applied distributed load. Here it means force per unit length of the beam, in the configuration u1, Rfield1. These are only forces, not moments.
Note
The force intensity must be uniform across the entire element. The force intensity is given in the global coordinates.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.gyroscopic — Method
gyroscopic(self::FEMMCorotBeam,  assembler::A,
   geom::NodalField{FFlt},
-  u::NodalField{T}) where {A<:AbstractSysmatAssembler, T<:Number}
Compute the quadratic-inertial-term (gyroscopic) mass matrix
This is a general routine for the abstract linear-deformation  FEMM.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_cartesian_to_natural! — Method
local_cartesian_to_natural!(aN, L)
Compute transformation from local Cartesian displacements to natural deformations of a beam element.
Matrix defined in Eq (4.8) of COMPUTER  METHODS  IN APPLIED  MECHANICS  AND  ENGINEERING   14  (1978)  401-451 ON LARGE  DISPLACEMENT-SMALL   STRAIN  ANALYSIS   OF  STRUCTURES WITH  ROTATIONAL   DEGREES  OF  FREEDOM. J.H.  ARGYRIS,   P.C.  DUNNE  and  D.W. SCHARPF
Arguments
L= current length of the element
Outputs
aN= transformation matrix to take Cartesian (local) displacement increments in the      element frame and to produce increments of natural deformations;      see local_frame_and_def! for the definition of the natural deformations
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_forces! — Method
local_forces!(FL, PN, L, aN)
Compute forces through which the element acts on the nodes in the local coordinate system.
Arguments
PN = column vector of natural forces; L= current length of the element, aN= transformation matrix to take Cartesian (local) displacement increments in the      element frame and to produce increments of natural deformations;      see local_frame_and_def! for the definition of the natural deformations
Outputs
FL = vector of forces acting on the nodes in the local coordinate system
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_frame_and_def! — Method
local_frame_and_def!(Ft, dN, F0, FtI, FtJ, x0, x1x2_vector, xt, RI, RJ)
Compute the current length of the element, the current element frame, and the natural deformations
Arguments
x0= array of node coordinates, one node per row, in initial configuration x1x2_vector= vector that lies in the x1-x2 local element coordinate      plane, in initial configuration xt= array of node coordinates, one node per row, in initial configuration RI,RJ=nodal rotation (orthogonal) matrix
Outputs
Lt= current length of the element, Ft= current element frame (orthogonal rotation matrix) whose columns are unit      vectors: they are centered halfway between the current locations of      the nodes, vector 1 points from node I to node J, vector 3 is      orthogonal to the sum of the nodal cross-section frame vectors 2 dN= vector of natural deformations; dN(1)= total change in length      between configurations 0 and t; dN(2)= symmetric bending;      dN(3)= anti-symmetric bending;    dN(4)= symmetric bending      dN(5)= anti-symmetric bending; dN(6)=total axial torsion angle.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_geometric_stiffness! — Method
local_geometric_stiffness!(SM, A, I2, I3, PN, L)
Compute the local geometric stiffness matrix.
Arguments
A= cross-sectional area, I2, I3=central moment of inertia of the cross-section about the x2 and x3 coordinate axis, PN= vector of natural forces; see natural_forces() for definitions L= current length of the element,
Outputs
SM = local geometric stiffness matrix, 12 x 12
This geometric stiffness matrix this consistent with relationship between the natural deformations and the natural forces that assumes there is only a linear constitutive link: no non-constitutive effects (bowing etc.) are included. This form of the geometric matrix was derived by Krenk. @BOOK{Krenk:2009,   AUTHOR =       {S. Krenk},   TITLE =        {Non-linear Modeling and Analysis of Solids and Structures },   PUBLISHER =    {Cambridge University Press},   YEAR =         {2009},   isbn =         {9780521830546} }
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_mass! — Method
local_mass!(MM, A, I1, I2, I3, rho, L, mass_type)
Mass matrix of the beam.
Arguments
A= cross-sectional area, I1=central moment of inertia of the cross-section about the x1 axis, I2, I3=central moment of inertia of the cross-section about the x2 and x3 coordinate axis, rho=mass density, L= initial length of the element,
Outputs
MM = local mass matrix, 12 x 12 In the element frame the mass matrix is constant.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_stiffness! — Method
local_stiffness!(SM, E, G, A, I2, I3, J, A2s, A3s, L, aN, DN)
Compute the local elastic stiffness matrix.
Arguments
E, G= Young's and shear modulus, A= cross-sectional area, I2, I3=central moment of inertia of the cross-section about the x2 and x3 coordinate axis, J=St Venant torsion constant, L= current length of the element,
Outputs
SM = local stiffness matrix, 12 x 12
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.mass — Method
mass(self::FEMMCorotBeam,  assembler::A,
+  u::NodalField{T}) where {A<:AbstractSysmatAssembler, T<:Number}
Compute the quadratic-inertial-term (gyroscopic) mass matrix
This is a general routine for the abstract linear-deformation  FEMM.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_cartesian_to_natural! — Method
local_cartesian_to_natural!(aN, L)
Compute transformation from local Cartesian displacements to natural deformations of a beam element.
Matrix defined in Eq (4.8) of COMPUTER  METHODS  IN APPLIED  MECHANICS  AND  ENGINEERING   14  (1978)  401-451 ON LARGE  DISPLACEMENT-SMALL   STRAIN  ANALYSIS   OF  STRUCTURES WITH  ROTATIONAL   DEGREES  OF  FREEDOM. J.H.  ARGYRIS,   P.C.  DUNNE  and  D.W. SCHARPF
Arguments
L= current length of the element
Outputs
aN= transformation matrix to take Cartesian (local) displacement increments in the      element frame and to produce increments of natural deformations;      see local_frame_and_def! for the definition of the natural deformations
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_forces! — Method
local_forces!(FL, PN, L, aN)
Compute forces through which the element acts on the nodes in the local coordinate system.
Arguments
PN = column vector of natural forces; L= current length of the element, aN= transformation matrix to take Cartesian (local) displacement increments in the      element frame and to produce increments of natural deformations;      see local_frame_and_def! for the definition of the natural deformations
Outputs
FL = vector of forces acting on the nodes in the local coordinate system
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_frame_and_def! — Method
local_frame_and_def!(Ft, dN, F0, FtI, FtJ, x0, x1x2_vector, xt, RI, RJ)
Compute the current length of the element, the current element frame, and the natural deformations
Arguments
x0= array of node coordinates, one node per row, in initial configuration x1x2_vector= vector that lies in the x1-x2 local element coordinate      plane, in initial configuration xt= array of node coordinates, one node per row, in initial configuration RI,RJ=nodal rotation (orthogonal) matrix
Outputs
Lt= current length of the element, Ft= current element frame (orthogonal rotation matrix) whose columns are unit      vectors: they are centered halfway between the current locations of      the nodes, vector 1 points from node I to node J, vector 3 is      orthogonal to the sum of the nodal cross-section frame vectors 2 dN= vector of natural deformations; dN(1)= total change in length      between configurations 0 and t; dN(2)= symmetric bending;      dN(3)= anti-symmetric bending;    dN(4)= symmetric bending      dN(5)= anti-symmetric bending; dN(6)=total axial torsion angle.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_geometric_stiffness! — Method
local_geometric_stiffness!(SM, A, I2, I3, PN, L)
Compute the local geometric stiffness matrix.
Arguments
A= cross-sectional area, I2, I3=central moment of inertia of the cross-section about the x2 and x3 coordinate axis, PN= vector of natural forces; see natural_forces() for definitions L= current length of the element,
Outputs
SM = local geometric stiffness matrix, 12 x 12
This geometric stiffness matrix this consistent with relationship between the natural deformations and the natural forces that assumes there is only a linear constitutive link: no non-constitutive effects (bowing etc.) are included. This form of the geometric matrix was derived by Krenk. @BOOK{Krenk:2009,   AUTHOR =       {S. Krenk},   TITLE =        {Non-linear Modeling and Analysis of Solids and Structures },   PUBLISHER =    {Cambridge University Press},   YEAR =         {2009},   isbn =         {9780521830546} }
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_mass! — Method
local_mass!(MM, A, I1, I2, I3, rho, L, mass_type)
Mass matrix of the beam.
Arguments
A= cross-sectional area, I1=central moment of inertia of the cross-section about the x1 axis, I2, I3=central moment of inertia of the cross-section about the x2 and x3 coordinate axis, rho=mass density, L= initial length of the element,
Outputs
MM = local mass matrix, 12 x 12 In the element frame the mass matrix is constant.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.local_stiffness! — Method
local_stiffness!(SM, E, G, A, I2, I3, J, A2s, A3s, L, aN, DN)
Compute the local elastic stiffness matrix.
Arguments
E, G= Young's and shear modulus, A= cross-sectional area, I2, I3=central moment of inertia of the cross-section about the x2 and x3 coordinate axis, J=St Venant torsion constant, L= current length of the element,
Outputs
SM = local stiffness matrix, 12 x 12
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.mass — Method
mass(self::FEMMCorotBeam,  assembler::A,
   geom::NodalField{FFlt},
-  u::NodalField{T}) where {A<:AbstractSysmatAssembler, T<:Number}
Compute the consistent mass matrix
This is a general routine for the abstract linear-deformation  FEMM.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.natural_forces! — Method
natural_forces!(PN, E, G, A, I2, I3, J, A2s, A3s, L, dN, DN)
Compute the natural forces from the natural deformations.
Argument
E, G= Young's and shear modulus, A= cross-sectional area, I2, I3=central moment of inertia of the cross-section about the x2 and x3 coordinate axis, J=St Venant torsion constant, L= current length of the element, dN= column vector of natural deformations; see local_frames()
Outputs
PN = column vector of natural forces;      PN[1]= axial force;      PN[2]= symmetric bending moment in the plane x1-x2;      PN[3]= anti-symmetric bending bending moment in the plane x1-x2;      PN[4]= symmetric bending bending moment in the plane x1-x3;      PN[5]= anti-symmetric bending bending moment in the plane x1-x3;      PN[6]= axial torque.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.natural_stiffness_Bernoulli! — Method
natural_stiffness_Bernoulli!(DN, E, G, A, I2, I3, J, A2s, A3s, L)
Compute the natural stiffness matrix.
function DN = natural_stiffness(self, E, G, A, I2, I3, J, L)
Arguments
  • E, G= Young's and shear modulus,
  • A= cross-sectional area,
  • I2, I3= central moment of inertia of the cross-section about the x2 and x3 coordinate axis,
  • J= St Venant torsion constant,
  • A2s = effective area for shear in the direction of x2 (ignored)
  • A3s = effective area for shear in the direction of x3 (ignored)
  • L= current length of the element,
Outputs
  • DN = 6 x 6 natural stiffness matrix
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.natural_stiffness_Timoshenko! — Method
natural_stiffness_Timoshenko!(DN, E, G, A, I2, I3, J, A2s, A3s, L)
Compute the natural stiffness matrix.
function DN = natural_stiffness(self, E, G, A, I2, I3, J, L)
Arguments
  • E, G= Young's and shear modulus,
  • A= cross-sectional area,
  • I2, I3= central moment of inertia of the cross-section about the x2 and x3 coordinate axis,
  • J= St Venant torsion constant,
  • A2s = effective area for shear in the direction of x2
  • A3s = effective area for shear in the direction of x3
  • L= current length of the element,
Outputs
  • DN = 6 x 6 natural stiffness matrix
source
FEMMShellT3FFModule functions
FinEtools.FEMMBaseModule.inspectintegpoints — Method
inspectintegpoints(self::AbstractFEMMDeforLinear,
+  u::NodalField{T}) where {A<:AbstractSysmatAssembler, T<:Number}
Compute the consistent mass matrix
This is a general routine for the abstract linear-deformation  FEMM.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.natural_forces! — Method
natural_forces!(PN, E, G, A, I2, I3, J, A2s, A3s, L, dN, DN)
Compute the natural forces from the natural deformations.
Argument
E, G= Young's and shear modulus, A= cross-sectional area, I2, I3=central moment of inertia of the cross-section about the x2 and x3 coordinate axis, J=St Venant torsion constant, L= current length of the element, dN= column vector of natural deformations; see local_frames()
Outputs
PN = column vector of natural forces;      PN[1]= axial force;      PN[2]= symmetric bending moment in the plane x1-x2;      PN[3]= anti-symmetric bending bending moment in the plane x1-x2;      PN[4]= symmetric bending bending moment in the plane x1-x3;      PN[5]= anti-symmetric bending bending moment in the plane x1-x3;      PN[6]= axial torque.
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.natural_stiffness_Bernoulli! — Method
natural_stiffness_Bernoulli!(DN, E, G, A, I2, I3, J, A2s, A3s, L)
Compute the natural stiffness matrix.
function DN = natural_stiffness(self, E, G, A, I2, I3, J, L)
Arguments
  • E, G= Young's and shear modulus,
  • A= cross-sectional area,
  • I2, I3= central moment of inertia of the cross-section about the x2 and x3 coordinate axis,
  • J= St Venant torsion constant,
  • A2s = effective area for shear in the direction of x2 (ignored)
  • A3s = effective area for shear in the direction of x3 (ignored)
  • L= current length of the element,
Outputs
  • DN = 6 x 6 natural stiffness matrix
source
FinEtoolsFlexStructures.FEMMCorotBeamModule.natural_stiffness_Timoshenko! — Method
natural_stiffness_Timoshenko!(DN, E, G, A, I2, I3, J, A2s, A3s, L)
Compute the natural stiffness matrix.
function DN = natural_stiffness(self, E, G, A, I2, I3, J, L)
Arguments
  • E, G= Young's and shear modulus,
  • A= cross-sectional area,
  • I2, I3= central moment of inertia of the cross-section about the x2 and x3 coordinate axis,
  • J= St Venant torsion constant,
  • A2s = effective area for shear in the direction of x2
  • A3s = effective area for shear in the direction of x3
  • L= current length of the element,
Outputs
  • DN = 6 x 6 natural stiffness matrix
source
FEMMShellT3FFModule functions
FinEtools.FEMMBaseModule.inspectintegpoints — Method
inspectintegpoints(self::AbstractFEMMDeforLinear,
   geom::NodalField{FFlt},  u::NodalField{TI},
   dT::NodalField{FFlt},
   felist::FIntVec,
   inspector::F,  idat, quantity=:Cauchy;
-  context...) where {TI<:Number, F<:Function}
Inspect integration point quantities.
  • geom - reference geometry field
  • u - displacement+rotation field
  • dT - temperature difference field
  • felist - indexes of the finite elements that are to be inspected:    The fes to be included are: fes[felist].
  • context    - structure: see the update!() method of the material.
  • inspector - function with the signature       idat = inspector(idat, j, conn, x, out, loc);  where   idat - a structure or an array that the inspector may          use to maintain some state,  for instance minimum or maximum of          stress, j is the element number, conn is the element connectivity,          out is the output of the update!() method,  loc is the location          of the integration point in the reference configuration.
Return
The updated inspector data is returned.
source
FinEtoolsFlexStructures.FEMMShellT3FFModule.mass — Method
mass(self::FEMMShellT3FF,  assembler::A,  geom::NodalField{FFlt}, dchi::NodalField{TI}) where {A<:AbstractSysmatAssembler, TI<:Number}
Compute the diagonal (lumped) mass matrix
The mass matrix can be expected to be non-singular.
source
FinEtoolsFlexStructures.FEMMShellT3FFModule.stiffness — Method
stiffness(self::FEMMShellT3FF, assembler::ASS, geom0::NodalField{FFlt}, u1::NodalField{TI}, Rfield1::NodalField{TI}, dchi::NodalField{TI}) where {ASS<:AbstractSysmatAssembler, TI<:Number}
Compute the material stiffness matrix.
source
FEMMShellT3FFCompModule functions
FinEtools.FEMMBaseModule.inspectintegpoints — Method
inspectintegpoints(self::AbstractFEMMDeforLinear,
+  context...) where {TI<:Number, F<:Function}
Inspect integration point quantities.
  • geom - reference geometry field
  • u - displacement+rotation field
  • dT - temperature difference field
  • felist - indexes of the finite elements that are to be inspected:    The fes to be included are: fes[felist].
  • context    - structure: see the update!() method of the material.
  • inspector - function with the signature       idat = inspector(idat, j, conn, x, out, loc);  where   idat - a structure or an array that the inspector may          use to maintain some state,  for instance minimum or maximum of          stress, j is the element number, conn is the element connectivity,          out is the output of the update!() method,  loc is the location          of the integration point in the reference configuration.
Return
The updated inspector data is returned.
source
FinEtoolsFlexStructures.FEMMShellT3FFModule.mass — Method
mass(self::FEMMShellT3FF,  assembler::A,  geom::NodalField{FFlt}, dchi::NodalField{TI}) where {A<:AbstractSysmatAssembler, TI<:Number}
Compute the diagonal (lumped) mass matrix
The mass matrix can be expected to be non-singular.
source
FinEtoolsFlexStructures.FEMMShellT3FFModule.stiffness — Method
stiffness(self::FEMMShellT3FF, assembler::ASS, geom0::NodalField{FFlt}, u1::NodalField{TI}, Rfield1::NodalField{TI}, dchi::NodalField{TI}) where {ASS<:AbstractSysmatAssembler, TI<:Number}
Compute the material stiffness matrix.
source
FEMMShellT3FFCompModule functions
FinEtools.FEMMBaseModule.inspectintegpoints — Method
inspectintegpoints(self::AbstractFEMMDeforLinear,
   geom::NodalField{FFlt},  u::NodalField{TI},
   dT::NodalField{FFlt},
   felist::FIntVec,
   inspector::F,  idat, quantity=:Cauchy;
-  context...) where {TI<:Number, F<:Function}
Inspect integration point quantities.
  • geom - reference geometry field
  • u - displacement+rotation field
  • dT - temperature difference field
  • felist - indexes of the finite elements that are to be inspected:    The fes to be included are: fes[felist].
  • context    - structure: see the update!() method of the material.
  • inspector - function with the signature       idat = inspector(idat, j, conn, x, out, loc);  where   idat - a structure or an array that the inspector may          use to maintain some state,  for instance minimum or maximum of          stress, j is the element number, conn is the element connectivity,          out is the output of the update!() method,  loc is the location          of the integration point in the reference configuration.
Return
The updated inspector data is returned.
source
FinEtoolsFlexStructures.FEMMShellT3FFCompModule.mass — Method
mass(self::FEMMShellT3FFComp,  assembler::A,  geom::NodalField{FFlt}, dchi::NodalField{TI}) where {A<:AbstractSysmatAssembler, TI<:Number}
Compute the diagonal (lumped) mass matrix
The mass matrix can be expected to be non-singular.
source
FEMMPointMassModule functions
FinEtoolsFlexStructures.FEMMPointMassModule.mass — Method
mass(self::FEMMCorotBeam,  assembler::A,
+  context...) where {TI<:Number, F<:Function}
Inspect integration point quantities.
  • geom - reference geometry field
  • u - displacement+rotation field
  • dT - temperature difference field
  • felist - indexes of the finite elements that are to be inspected:    The fes to be included are: fes[felist].
  • context    - structure: see the update!() method of the material.
  • inspector - function with the signature       idat = inspector(idat, j, conn, x, out, loc);  where   idat - a structure or an array that the inspector may          use to maintain some state,  for instance minimum or maximum of          stress, j is the element number, conn is the element connectivity,          out is the output of the update!() method,  loc is the location          of the integration point in the reference configuration.
Return
The updated inspector data is returned.
source
FinEtoolsFlexStructures.FEMMShellT3FFCompModule.mass — Method
mass(self::FEMMShellT3FFComp,  assembler::A,  geom::NodalField{FFlt}, dchi::NodalField{TI}) where {A<:AbstractSysmatAssembler, TI<:Number}
Compute the diagonal (lumped) mass matrix
The mass matrix can be expected to be non-singular.
source
FEMMPointMassModule functions
FinEtoolsFlexStructures.FEMMPointMassModule.mass — Method
mass(self::FEMMCorotBeam,  assembler::A,
   geom::NodalField{FFlt},
-  u::NodalField{T}) where {A<:AbstractSysmatAssembler, T<:Number}
Compute the consistent mass matrix
This is a general routine for the abstract linear-deformation  FEMM.
source
FEMMPointGroundedSpringModule functions
FEMMPointGroundedSpringModule functions
RotUtilModule functions
VisUtilModule functions
Modules = [VisualStructures]
+  u::NodalField{T}) where {A<:AbstractSysmatAssembler, T<:Number}
Compute the stiffness matrix
source

RotUtilModule functions

VisUtilModule functions

Modules = [VisualStructures]
 Private = true
-Order = [:function]

TransformerModule functions

+Order = [:function]

TransformerModule functions

diff --git a/dev/man/reference.html b/dev/man/reference.html index c88c585..26c3cd5 100644 --- a/dev/man/reference.html +++ b/dev/man/reference.html @@ -1,2 +1,2 @@ -Reference · FinEtoolsFlexStructures.jl
Edit on GitHub
+Reference · FinEtoolsFlexStructures.jl
Edit on GitHub
diff --git a/dev/man/types.html b/dev/man/types.html index bcc5e8b..14e1a69 100644 --- a/dev/man/types.html +++ b/dev/man/types.html @@ -1,4 +1,4 @@ -Types · FinEtoolsFlexStructures.jl
Edit on GitHub

Types

Table of Contents

CrossSectionModule types

CompositeLayupModule types

FinEtoolsFlexStructures.CompositeLayupModule.CompositeLayup — Method
CompositeLayup(name, plies, mcsys)

Create a composite layup.

Provide the name, the array of plies, and the coordinate system that defines the orientation of the composite layup. The first base spector of this coordinate system is the reference direction for the layup.

source
FinEtoolsFlexStructures.CompositeLayupModule.Ply — Method
Ply{M} <: AbstractPly

Create a ply.

Provide name, material of the ply, thickness of the ply, an angle between the first bases vector of the layup coordinate system and the first direction of the ply material coordinate system.

source

FESetShellT3Module types

MeshFrameMemberModule types

FEMMCorotBeamModule types

FEMMShellT3FFModule types

FinEtoolsFlexStructures.FEMMShellT3FFModule.FEMMShellT3FF — Type
FEMMShellT3FF{S<:FESetT3, F<:Function} <: AbstractFEMM

Class for the finite element modeling machine of the T3 triangular Flat-Facet shell with the Discrete Shear Gap technology and a consistent handling of the normals.

With averaging of the transverse strain-displacement matrix or averaging of the transverse shear stiffness matrix to provide isotropic transverse shear response.

Also, the formulation is developed to correctly handle the coupling of twisting moments and transverse shear (such as in the twisted beam or the Raasch hook problems) by incorporating "nodal" normals.

Some of the programming developed consistently with the paper

[1] Cui et al, Analysis of plates and shells using an edge-based smoothed finite element method, Comput Mech (2010) 45:141–156 DOI 10.1007/s00466-009-0429-9

The stabilization factor of the shear term of

[2] Mikko Lyly, Rolf Stenberg and Teemu Vihinen, A stable bilinear element for the Reissner-Mindlin plate model Computer Methods in Applied Mechanics and Engineering 110 (1993) 343-357

is incorporated. Refer to expressions (3.12) and (3.13).

The treatment of the transformation between the element and nodal coordinates is carried out using a clean alternative to the publication

[3] Finite Elements in Analysis and Design 30 (1998) 235—242 The treatment of shell normals in finite element analysis Richard H. MacNeal, Charles T. Wilson, Robert L. Harder, Claus C. Hoff The MacNeal-Schwendler Corporation, 815 Colorado Blvd., Los Angeles, CA 90041, USA

The formula for the element to nodal basis transformation is derived from the expression

[theta]_n = [A]_E^T [theta]_e + [A_3,1:3]_E^T [alpha_3]_e

by disconnecting the drilling degree of freedom from the bending degrees of freedom in the nodal basis.

The following features are incorporated to deal with nodal normals:

  • Nodal normals are averages of the normals of elements that meet at a node.
  • A crease in the surface is taken into account. In that case the normal are not averaged across the crease. At the nodes along the crease every element uses the normal to its surface instead of the nodal normal.

Configuration:

These attributes of the FEMM can be set after it's been created.

  • transv_shear_formulation: which formulation for the transverse shear stiffness?
    • FEMMShellT3FFModule.__TRANSV_SHEAR_FORMULATION_AVERAGE_B - averaged strains (default)
    • FEMMShellT3FFModule.__TRANSV_SHEAR_FORMULATION_AVERAGE_K - averaged stiffness
  • drilling_stiffness_scale: multiplier of the generalized stiffness coefficient
  • threshold_angle: angle in degrees. If a nodal normal subtends angle bigger then this threshold, the nodal normal at that note is marked as invalid.
  • mult_el_size: multiplier of the square of the element size, used to control transverse shear stiffness.
source

FEMMShellT3FFCompModule types

FinEtoolsFlexStructures.FEMMShellT3FFCompModule.FEMMShellT3FFComp — Type
FEMMShellT3FFComp{S<:FESetT3, F<:Function} <: AbstractFEMM

Class for the finite element modeling machine of the T3 triangular Flat-Facet shell with the Discrete Shear Gap technology and a consistent handling of the normals. This formulation is suitable for modelling of COMPOSITE (layered) materials.

For details for the homogeneous-shell refer to FEMMShellT3FF.

source

FEMMPointMassModule types

FEMMPointGroundedSpringModule types

RotUtilModule types

VisUtilModule types

Modules = [VisualStructures]
+Types · FinEtoolsFlexStructures.jl
Edit on GitHub
Types
Table of Contents
CrossSectionModule types
CompositeLayupModule types
FinEtoolsFlexStructures.CompositeLayupModule.CompositeLayup — Method
CompositeLayup(name, plies, mcsys)
Create a composite layup.
Provide the name, the array of plies, and the coordinate system that defines the orientation of the composite layup. The first base spector of this coordinate system is the reference direction for the layup.
source
FinEtoolsFlexStructures.CompositeLayupModule.Ply — Method
Ply{M} <: AbstractPly
Create a ply.
Provide name, material of the ply, thickness of the ply, an angle between the first bases vector of the layup coordinate system and the first direction of the ply material coordinate system.
source
FESetShellT3Module types
MeshFrameMemberModule types
FEMMCorotBeamModule types
FEMMShellT3FFModule types
FinEtoolsFlexStructures.FEMMShellT3FFModule.FEMMShellT3FF — Type
FEMMShellT3FF{S<:FESetT3, F<:Function} <: AbstractFEMM
Class for the finite element modeling machine of the T3 triangular Flat-Facet shell with the Discrete Shear Gap technology and a consistent handling of the normals. 
With averaging of the transverse strain-displacement matrix or averaging of the transverse shear stiffness matrix to provide isotropic transverse shear response. 
Also, the formulation is developed to correctly handle the coupling of twisting moments and transverse shear (such as in the twisted beam or the Raasch hook problems) by incorporating "nodal" normals.
Some of the programming developed consistently with the paper
[1] Cui et al, Analysis of plates and shells using an edge-based smoothed finite element method, Comput Mech (2010) 45:141–156 DOI 10.1007/s00466-009-0429-9
The stabilization factor of the shear term of
[2] Mikko Lyly, Rolf Stenberg and Teemu Vihinen, A stable bilinear element for the Reissner-Mindlin plate model Computer Methods in Applied Mechanics and Engineering 110 (1993) 343-357 
is incorporated. Refer to expressions (3.12) and (3.13).
The treatment of the transformation between the element and nodal coordinates is carried out using a clean alternative to the publication
[3] Finite Elements in Analysis and Design 30 (1998) 235—242 The treatment of shell normals in finite element analysis Richard H. MacNeal, Charles T. Wilson, Robert L. Harder, Claus C. Hoff The MacNeal-Schwendler Corporation, 815 Colorado Blvd., Los Angeles, CA 90041, USA
The formula for the element to nodal basis transformation is derived from the expression
[theta]_n = [A]_E^T [theta]_e + [A_3,1:3]_E^T [alpha_3]_e
by disconnecting the drilling degree of freedom from the bending degrees of freedom in the nodal basis.
The following features are incorporated to deal with nodal normals:
  • Nodal normals are averages of the normals of elements that meet at a node.
  • A crease in the surface is taken into account. In that case the normal are not averaged across the crease. At the nodes along the crease every element uses the normal to its surface instead of the nodal normal.
Configuration:
These attributes of the FEMM can be set after it's been created.
  • transv_shear_formulation: which formulation for the transverse shear stiffness? 
    • FEMMShellT3FFModule.__TRANSV_SHEAR_FORMULATION_AVERAGE_B - averaged strains (default)
    • FEMMShellT3FFModule.__TRANSV_SHEAR_FORMULATION_AVERAGE_K - averaged stiffness
  • drilling_stiffness_scale: multiplier of the generalized stiffness coefficient
  • threshold_angle: angle in degrees. If a nodal normal subtends angle bigger then this threshold, the nodal normal at that note is marked as invalid.
  • mult_el_size: multiplier of the square of the element size, used to control transverse shear stiffness.
source
FEMMShellT3FFCompModule types
FinEtoolsFlexStructures.FEMMShellT3FFCompModule.FEMMShellT3FFComp — Type
FEMMShellT3FFComp{S<:FESetT3, F<:Function} <: AbstractFEMM
Class for the finite element modeling machine of the T3 triangular Flat-Facet shell with the Discrete Shear Gap technology and a consistent handling of the normals. This formulation is suitable for modelling of COMPOSITE (layered) materials. 
For details for the homogeneous-shell refer to FEMMShellT3FF.
source
FEMMPointMassModule types
FEMMPointGroundedSpringModule types
RotUtilModule types
VisUtilModule types
Modules = [VisualStructures]
 Private = true
-Order = [:type]
TransformerModule types

+Order = [:type]

TransformerModule types

diff --git a/dev/search.html b/dev/search.html index cf43073..072cae9 100644 --- a/dev/search.html +++ b/dev/search.html @@ -1,2 +1,2 @@ -Search · FinEtoolsFlexStructures.jl

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    +Search · FinEtoolsFlexStructures.jl

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