dktplate

2D Discrete Kirchhoff Triangular plate element

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Three dofs (w-displacement, u and v - rotations) are required in each node.

Quadratic approximation of rotations, cubic approximation of displacement along the edges. Note: there is no need to define interpolation for displacement on the element.

Default integration of all terms using three point formula.

Layered cross section support.

Cross section thickness is required.

Body loads are supported. Boundary load support is beta.

On output, the generalized shell strain/force momentum vectors in global coordinate system are printed, with the following meaning:

where ε_x,ε_y,ε_xy are membrane in plane normal deformations, γ_zx,γ_xz are (out of plane and in plane) shear componets, κ_x,κ_y,κ_xy are curvatures, n_x,n_y,n_xy,q_xz,q_yz are integral forces (normal and shear forces), and m_x,m_y,m_xy are bending moments. Please note, for example, that bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer.

0.

Reliable

tests/sm/patch_dkt.in, tests/sm/dkt_bending01.in

J.L.Batoz, K.J.Bathe, L.W.Ho: A study of three-node triangular plate bending elements, IJNME, 15(12):1771-1812, 1980

qdktplate

2D Discrete Kirchhoff Quad plate element

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Three dofs (w-displacement, u and v - rotations) are required in each node.

Quadratic approximation of rotations, cubic approximation of displacement along the edges. Note: there is no need to define interpolation for displacement on the element.

Default integration of all bending terms using four point formula.

Layered cross section support.

Cross section thickness is required.

Body loads are supported.

On output, the generalized shell strain/force momentum vectors in global coordinate system are printed, with the following meaning:

where ε_x,ε_y,ε_xy are membrane in plane normal deformations, γ_zx,γ_xz are (out of plane and in plane) shear componets, κ_x,κ_y,κ_xy are curvatures, n_x,n_y,n_xy,q_xz,q_yz are integral forces (normal and shear forces), and m_x,m_y,m_xy are bending moments. Please note, for example, that bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer.

0.

Reliable

tests/sm/patch_qdtk.in

J.L.Batoz, K.J.Bathe, L.W.Ho: A study of three-node triangular plate bending elements, IJNME, 15(12):1771-1812, 1980

cctplate

2D constant curvature triangular plate element

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Three dofs (w-displacement, u and v - rotations) are required in each node.

Linear approximation of rotations, quadratic approximation of displacement.

Integration of all terms using one point formula.

Layered cross section support.

Cross section thickness is required.

Body loads are supported. Boundary loads are not supported now.

On output, the generalized shell strain/force momentum vectors in global coordinate system are printed, with the following meaning:

where ε_x,ε_y,ε_xy are membrane in plane normal deformations, γ_zx,γ_xz are (out of plane and in plane) shear componets, κ_x,κ_y,κ_xy are curvatures, n_x,n_y,n_xy,q_xz,q_yz are integral forces (normal and shear forces), and m_x,m_y,m_xy are bending moments. Please note, for example, that bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer.

0.

Reliable

tests/sm/patch_cct.in, tests/sm/patch_cct_02.in, tests/sm/patch200.in

cctplate3d

Constant curvature triangular plate element in arbitray position

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Six dofs (u,v,w-displacements and u,v,w rotations) are in general required in each node.

Linear approximation of ratations, quadratic approximation of displacement.

Integration of all terms using one point formula.

Layered cross section support.

Cross section thickness is required.

Body loads are supported. Boundary loads are not supported now.

On output, the shell force (s_f), shell strain (s_s), shell momentum (s_m), and shell curvature (s_c) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:

where ε_x,ε_y,ε_z are membrane normal deformations, γ_zy,γ_zx,γ_xy are (out of plane and in plane) shear componets, κ_x,κ_y,κ_z,κ_yz,κ_xz,κ_xy are curvatures, n_x,n_y,n_z,v_yz,v_xz,v_xy are integral forces (normal and shear forces), and m_x,m_y,m_z,m_yz,m_xz,m_xy are bending moments. Please note, for example, that bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer.

0.

Reliable

tests/sm/patch_cct3d.in

rershell

Simple shell based on combination of CCT plate element (Mindlin hypothesis) with triangular plane stress element. element can be arbitrary positioned in space.

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Six dofs (u,v,w-displacements and u,v,w rotations) are in general required in each node. Note, that although element it requires generally six DOFs per node, no stiffness to local rotation along z-axis (rotation around element normal) is supplied.

Linear approximation of ratations, quadratic approximation of displacement.

Integration of all terms using one point formula.

Layered cross section support.

Cross section thickness is required.

Body loads are supported. Boundary loads are not supported now.

On output, the shell force (s_f), shell strain (s_s), shell momentum (s_m), and shell curvature (s_c) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:

where ε_x,ε_y,ε_z are membrane normal deformations, γ_zy,γ_zx,γ_xy are (out of plane and in plane) shear componets, κ_x,κ_y,κ_z,κ_yz,κ_xz,κ_xy are curvatures, n_x,n_y,n_z,v_yz,v_xz,v_xy are integral forces (normal and shear forces), and m_x,m_y,m_z,m_yz,m_xz,m_xy are bending moments. Please note, for example, that bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer.

0.

Reliable

tests/sm/patch_rershell.in

tr_shell11

Triangular shell element combining CCT3D plate element (Mindlin hypothesis) with triangular plane stress element with rotational DOFs

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Six dofs (u,v,w-displacements and u,v,w rotations) are in general required in each node.

See description of cct and trplanstrrot elements

Four point integration, reduced integration of strain associated to normal rotation and shear terms.

Layered cross section support.

Cross section thickness is required.

Body loads are supported. Boundary loads are supported (only surface loads).

On output, the shell force (s_f), shell strain (s_s), shell momentum (s_m), and shell curvature (s_c) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:

where ε_x,ε_y,ε_z are membrane normal deformations, γ_zy,γ_zx,γ_xy are (out of plane and in plane) shear componets, κ_x,κ_y,κ_z,κ_yz,κ_xz,κ_xy are curvatures, n_x,n_y,n_z,v_yz,v_xz,v_xy are integral forces (normal and shear forces), and m_x,m_y,m_z,m_yz,m_xz,m_xy are bending moments. Please note, for example, that bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer.

0.

Reliable

tests/sm/trshell11_1.in

tr_shell02

Triangular shell element combining DKT plate element with triangular plane stress element with rotational DOFs

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Six dofs (u,v,w-displacements and u,v,w rotations) are in general required in each node.

See description of cct and trplanstrrot elements

4 integration points necessary, use ”NIP 4” in element record.

Cross section thickness is required.

Body loads are supported. Boundary loads are supported (only surface loads).

On output, the shell force (s_f), shell strain (s_s), shell momentum (s_m), and shell curvature (s_c) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:

where ε_x,ε_y,ε_z are membrane normal deformations, γ_zy,γ_zx,γ_xy are (out of plane and in plane) shear componets, κ_x,κ_y,κ_z,κ_yz,κ_xz,κ_xy are curvatures, n_x,n_y,n_z,v_yz,v_xz,v_xy are integral forces (normal and shear forces), and m_x,m_y,m_z,m_yz,m_xz,m_xy are bending moments. Please note, for example, that bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer.

0.

-

Works only with linear material models, as bending and membrane actions are uncoupled

tests/sm/trshell02_test.in

quad1mindlin

Quadrilateral, bilinear, four-node Mindlin plate

[NIP #(in)]

Three dofs (w-displacement, u and v - rotation) are required in each node.

Linear for all unknowns.

Default uses 4 integration points. No reduced integration is used, as it causes numerical problems.

Layered cross section support.

Cross section thickness is required.

Dead weight loads, and edge loads are supported.

On output, the generalized shell strain/force momentum vectors in global coordinate system are printed, with the following meaning:

where ε_x,ε_y,ε_xy are membrane in plane normal deformations, γ_zx,γ_xz are (out of plane and in plane) shear componets, κ_x,κ_y,κ_xy are curvatures, n_x,n_y,n_xy,q_xz,q_yz are integral forces (normal and shear forces), and m_x,m_y,m_xy are bending moments. Please note, for example, that bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer.

0.

[1]

Experimental

tests/sm/patch_quad1mindlin.in

tr2shell7

Triangular, quadratic, six-node shell with 7 dofs/node

[NIP #(in)]

Seven dofs (displacement in u, v and w-direction; change in director field in u, v and w-direction; and inhomgenous thickness stretch) are required in each node.

Quadratic for all unknowns.

Default uses 6 integration points in the midsurface plane. Number of integration points in the thickness direction is determined by the Layered cross section.

Layered cross section support.

This element must be used with a Layered cross section.

Edge loads, constant pressure loads and surface loads are supported.

Not applicable. The implementation is for large defomrations and hence geometrical nonlinearities will always be present, regardless the value of Nlgeo.

[3]

Experimental

tests/sm/staggeredsolver.in

mitc4shell

Quadrilateral, bilinear, four-node shell element using the MITC technique.

[NIP #(in)] [NIPZ #(in)] [directorType #(in)]

NIP: allows to set the number of integration points in local x-y plane (default 4).

NIPZ: allows to set the number of integration points in local z-direction (default 2).

directorType: allows to set director vectors. Director vectors can be set as normal to the plane (directorType = 0, default), or calculated for each node as an average of neighbouring elements of same crosssection (directorType = 1), or can be specified at crosssection (directorType =2).

Six dofs (u,v,w-displacements and u,v,w rotations) are in general required in each node. Note, that although element requires generally six DOFs per node, no stiffness to local rotation along z-axis (rotation around director vector) is supplied.

Linear approximation of displacements and rotations.

Integration of all terms using Gauss integration formula in 8 points (default) or specified using NIP and NIPZ parameters.

Variable cross section support.

Cross section thickness is required (measured along director vector). Director vectors components may be specified [directorx #(in)][directory #(in)][directorz #(in)] in case of directorType 2.

Body and boundary loads are supported.

On output, the shell force (s_f), shell momentum (s_m), shell strain (s_s), shell curvature (s_c), strain (ε), and stress (σ) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:

where n_x,n_y,n_z,v_yz,v_xz,v_xy are integral forces (normal and shear forces), and m_x,m_y,m_z,m_yz,m_xz,m_xy are bending moments, ε_x,ε_y,ε_z are membrane normal deformations, γ_zy,γ_zx,γ_xy are (out of plane and in plane) shear componets, κ_x,κ_y,κ_z,κ_yz,κ_xz,κ_xy are curvatures. Please note, for example, the bending moment m_x is defined as m_x = ∫ σ_xz dz, so it acts along the y-axis and positive value causes tension in bottom layer (positive z-coordinate). The shell force (s_f), shell momentum (s_m), shell strain (s_s), and shell curvature (s_c) tensors are evaluated at the midplane of the element (thus are constant along the thickness) while the strain (ε), and stress (σ) tensors are evaluated at each Gausspoint.

0.

-

tests/sm/patch_mitc4.in, tests/sm/patch_mitc4_02.in, tests/sm/scordelis_mitc4.in

quad1plateSubsoil

Quadrilateral, bilinear, four-node sub-soil plate element

One dof (w-displacement) is required in each node.

Linear for transwersal displacement.

4 integration points.

Surface load support.

Requires material model with 2dPlateSubSoil mode support.

[2]

tests/sm/test_wp1.in, tests/sm/test_wp5.in

tria1platesubsoil

Tringular, three-node sub-soil plate element with linear interpolation

One dof (w-displacement) is required in each node.

Linear for transwersal displacement.

1 integration points.

Surface load support.

Requires material model with 2dPlateSubSoil mode support.

[2]

tests/sm/test_wp2.in, tests/sm/test_wp5.in