SHELL163 Element Description

SHELL163 is a 4-node element with both bending and membrane capabilities. Both in-plane and normal loads are permitted. The element has 12 degrees of freedom at each node: translations, accelerations, and velocities in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes.

This element is used in explicit dynamic analyses only. Refer to the LS-DYNA Theoretical Manual for more information.

Figure 163.1:  SHELL163 Geometry

SHELL163 Input Data

The following real constants are provided for SHELL163. SHRF is the shear factor. NIP is the number of integration points through the thickness of the element, up to a maximum of 100. If NIP is input as 0 or blank, ANSYS defaults the value to 2. T1 - T4 indicate the shell thickness at each of the 4 nodes. NLOC specifies the location of the reference surface for KEYOPT(1) = 1, 6, or 7. The reference surface is used in the formulation of the element stiffness matrix. (NLOC does not define the location of the contact surface.) If you set NLOC = 1 or -1 (top or bottom surface), you must set SHNU = -2 on the EDSHELL command.

ESOP is the option for the spacing of integration points, and can be either 0 or 1. ESOP is used only if KEYOPT(4) > 0. If you set ESOP = 0, you must define real constants S(i), and WF(i) to define the integration point locations. If KEYOPT(3) = 1, then you must also define BETA(i) and MAT(i) for each integration point. Set ESOP = 1 if the integration points are equally spaced through the thickness such that the shell is subdivided into NIP layers of equal thickness (up to 100 layers).

The thickness is assumed to vary smoothly over the area of the element, with the thickness input at the 4 nodes. If the element has a constant thickness, only TK(I) need be input. If the thickness is not constant, all four thicknesses must be input.

If you set ESOP = 0 and define the integration points using S(i), and WF(i), and possibly BETA(i) and MAT(i), note the following:

S(i) is the relative coordinate of the integration point and must be within the range -1 to 1. WF(i) is the weighting factor for the i-th integration point. It is calculated by dividing the thickness associated with the integration point by the actual shell thickness (that is, Δt_i/t); see Figure 163.2: Arbitrary Ordering of Integration Points for User Defined Shell Integration Rule. In the user defined shell integration rule, the ordering of the integration points is arbitrary. If using these real constants to define integration points, then S(i) and WF(i) must both be specified for each integration point (maximum of 100). BETA(i) is the material angle (in degrees) at the i-th integration point and must be specified for each integration point. The material model is not allowed to change within an element, although the material properties (EX, NUXY, etc.), as defined per MAT(i), can change. However, the density may not vary through the thickness of the shell element. If more than one material is used, and the densities vary between materials, the density of the material of the first layer will be used for the entire element.

If KEYOPT(4) = 0, the integration rule is defined by KEYOPT(2). The Gauss rule (KEYOPT(2) = 0) is valid for up to five layers (integration points). The trapezoidal rule (KEYOPT(2) = 1) allows up to 100 layers, but is not recommended for less than 20 layers, especially if bending is involved.

Figure 163.2:  Arbitrary Ordering of Integration Points for User Defined Shell Integration Rule

Use the EDLOAD command to apply nodal loads and other load types described below. For detailed information on how to apply loads in an explicit dynamic analysis, see Loading in the ANSYS LS-DYNA User's Guide.

Pressures can be input as surface loads on the element midsurfaces. Positive normal pressures act into the element (that is, positive pressure acts in the negative z direction). Note, however, that pressure is actually applied to the midsurface. See Figure 163.3: Nodal Numbering for Pressure Loads (Positive Pressure Acts in Negative Z Direction).

Figure 163.3:  Nodal Numbering for Pressure Loads (Positive Pressure Acts in Negative Z Direction)

Base accelerations and angular velocities in the x, y, and z directions can be applied at the nodes using the EDLOAD command. To apply these loads, you need to first select the nodes and create a component. The load is then applied to that component. Each node in the component will have the specified load.

You can also use the EDLOAD command to apply loads (displacements, forces, etc.) on rigid bodies.

Several types of temperature loading are also available for this element. See Temperature Loading in the ANSYS LS-DYNA User's Guide.

For this element, you can choose from the following materials:

The orthotropic elastic material model does not accept integration point angles (BETA(i)). Therefore, to model a composite material, you need to use the composite damage material model. If you do not wish to use the damage features of this material model, just set the required strength values to zero.

KEYOPT(1) allows you to specify 1 of 12 element formulations for SHELL163 (see "SHELL163 Input Summary"). A brief description about each element formulation follows:

The Hughes-Liu element formulation (KEYOPT(1) = 1) is based on a degenerated continuum formulation. This formulation results in substantially large computational costs, but it is effective when very large deformations are expected. This formulation treats warped configurations accurately but does not pass the patch test. It uses one-point quadrature with the same hourglass control as the Belytschko-Tsay.

The Belytschko-Tsay (default) element formulation (KEYOPT(1) = 0 or 2) is the fastest of the explicit dynamics shells. It is based on the Mindlin-Reissner assumption, so transverse shear is included. It does not treat warped configurations accurately, so it should not be used in coarse mesh models. One-point quadrature is used with hourglass control. A default value is set for the hourglass parameter. When hourglassing appears, you should increase this parameter to avoid hourglassing. It does not pass the patch test.

The BCIZ Triangular Shell element formulation (KEYOPT(1) = 3) is based on a Kirchhoff plate theory and uses cubic velocity fields. Three sets of quadrature points are used in each element, so it is relatively slow. It passes the patch test only when the mesh is generated from three sets of parallel lines.

The C⁰ Triangular Shell element formulation (KEYOPT(1) = 4) is based on a Mindlin-Reissner plate theory and uses linear velocity fields. One quadrature point is used in the element formulation. This formulation is rather stiff, so it should not be used for constructing an entire mesh, only to transition between meshes.

The Belytschko-Tsay membrane element formulation (KEYOPT(1) = 5) is the same as the Belytschko-Tsay but with no bending stiffness.

The S/R Hughes-Liu element formulation (KEYOPT(1) = 6) is the same as the Hughes-Liu, but instead of using one-point quadrature with hourglass control, this formulation uses selective reduced integration. This increases the cost by a factor of 3 to 4, but avoids certain hourglass modes; certain bending hourglass modes are still possible.

The S/R corotational Hughes-Liu element formulation (KEYOPT(1) = 7) is the same as the S/R Hughes-Liu except it uses the corotational system.

The Belytschko-Leviathan shell formulation (KEYOPT(1) = 8) is similar to the Belytschko-Wong-Chiang with one-point quadrature but it uses physical hourglass control, therefore no user-set hourglass control parameters need to be set.

The fully-integrated Belytschko-Tsay membrane element formulation (KEYOPT(1) = 9) is the same as the Belytschko-Tsay membrane except is uses a 2 x 2 quadrature instead of a one-point quadrature. This formulation is more robust for warped configurations.

The Belytschko-Wong-Chiang formulation (KEYOPT(1) = 10) is the same as the Belytschko-Tsay except the shortcomings in warped configuration are avoided. Costs about 10% more.

The fast (corotational) Hughes-Liu formulation (KEYOPT(1) = 11) is the same as the Hughes-Liu except this formulation uses the corotational system.

The fully-integrated Belytschko-Tsay shell element formulation (KEYOPT(1) = 12) uses a 2 x 2 quadrature in the shell plane and is about 2.5 times slower than KEYOPT(1) = 2. It is useful in overcoming hourglass modes. The shear locking is remedied by introducing an assumed strain for the transverse shear.

Of the twelve shell element formulations, only KEYOPT(1) = 1, 2, 6, 7, 8, 9, 10, 11, and 12 are valid for an explicit-to-implicit sequential solution. For metal forming analyses, KEYOPT(1) = 10 and 12 are recommended in order to properly account for warping.

When the Mooney-Rivlin Rubber material model is used with SHELL163 elements, the LS-DYNA code will automatically use a total Lagrangian modification of the Belytschko-Tsay formulation instead of using the formulation you specify via KEYOPT(1). This program-chosen formulation is required to address the special needs of the hyperelastic material.

A summary of the element input is given in "SHELL163 Input Summary". A general description of element input is given in Element Input.

SHELL163 Output Data

To store output data for this element, you must specify the number of output locations for which you want data using the EDINT,SHELLIP command during solution. To review the stored data for a specified layer, use the LAYER,NUM command. However, be aware that the output location for this data is always at the integration point. "Top" and "bottom" refer to the top or bottom integration point, which is not necessarily the top or bottom surface.

Stress data is always output from the bottom of the shell to the top. See Figure 163.2: Arbitrary Ordering of Integration Points for User Defined Shell Integration Rule.

In all cases (default and otherwise), strain is always output for two layers only: Layer 1 = bottom and layer 2 = top.

The number of integration points specified by real constant NIP controls the output locations through the thickness of the shell. If NIP = SHELLIP, then each layer corresponds to an integration point, and those are the locations where you will get output data. If NIP>SHELLIP, then data is output only at the SHELLIP number of locations (first bottom layer, then layers 2 through n moving up from the bottom). If NIP<SHELLIP (but NIP>2), then results are output only for NIP number of layers.

By default, the number of integration points (NIP) is 2, and the number of output locations/layers (SHELLIP) is 3. In this case, stress data is output in the following order: Layer 1 = bottom, layer 2 = middle, and layer 3 = top. When SHELLIP = 3, the middle layer will be an interpolated value if NIP is an even number or an actual value at an integration point if NIP is an odd number.

If NIP = 1, the integration point is at the element midplane, and only one stress and one strain value are output.

For elements with 2 x 2 integration points in the shell plane (KEYOPT(1) = 6, 7, 9, 12), LS-DYNA performs an averaging of any data output at those points in every layer so that the output is the same for all shell formulations.

For the default RSYS setting, strains (EPTO) and generalized stresses (M, T, N) are output in the element coordinate system, and stresses (S) are output in the global Cartesian system for all formulations associated with SHELL163, except the Hughes-Liu formulation. Strain output (EPTO) for the Hughes-Liu formulation (KEYOPT(1) = 1) is output in the global Cartesian system.

You can rotate stress results for this element into another coordinate system using the RSYS command. However, RSYS has no effect on the stress results for composite SHELL163 elements (KEYOPT(3) = 1). In addition, RSYS cannot be used to rotate strain results for any of the SHELL163 element formulations.

The following items are available in the results file.

Table 163.3: SHELL163 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 163.3: SHELL163 Item and Sequence Numbers:

The SMISC quantities in the above table are independent of layers (that is, you will get one set of SMISC quantities output per element). However, the NMISC items are layer-dependent, and the order of the NMISC items is dependent on the SHELLIP and NIP values. The order shown in the table corresponds to the default SHELLIP value (SHELLIP = 3). If NIP > 3, it is strongly recommended that you set SHELLIP = NIP. In this case, the ETABLE output will go from top (NMISC,1) to bottom (NMISC,n where n is the total number of layers). If SHELLIP is not equal to NIP, the order of NMISC items will vary. Therefore, you should not use ETABLE to access the NMISC items when NIP > 3 and SHELLIP is not equal to NIP.

SHELL163 Assumptions and Restrictions

SHELL163 Product Restrictions

There are no product-specific restrictions for this element.