Elastic, Damper, and Mass Elements

For such continuum elements, the displacement field over a volume of material which is represented by an element is approximated by corresponding shape functions based on the nodal coordinates. For example, in linear axial elements, the displacement vector is expressed as a linear polynomial whose constants are obtained from the nodal displacements.

Implementation

OptiStruct supports several elements, ranging from 0D, 1D, 2D, to 3D elements. Depending upon the type of analysis, modeling, the level of detail, and the computational time available, any of the available elements, or a combination of them can be selected to achieve the required results.

Zero-dimensional Elements

One-dimensional Elements

Two-dimensional Shell Elements

Two-dimensional shell elements are used to model thin-shell or thick-shell behavior. Thin-shell behavior can be applied to situations where transverse shear deformation in bending can be ignored, whereas, thick-shell behavior is required in applications where transverse shear appreciably affects model behavior. OptiStruct shell elements have the ability to incorporate in-plane or membrane actions, plane strain, and bending action (including transverse shear characteristics and membrane-bending coupling actions). Reissner-Mindlin shell theory is used to model bending. A plane-strain option is available for pure 2D applications. These properties can be controlled using the PSHELL Bulk Data Entry. For example, the MID# fields on the PSHELL, can be used to define material properties to include bending, transverse shear, membrane-bending coupling, and so on.

The element shapes may be triangular (CTRIA3) or quadrilateral (CQUAD4). Second order triangular (CTRIA6) and quadrilateral (CQUAD8) shell elements are also available.

The first order shell element formulation for CQUAD4 and CTRIA3 has the special characteristic of using six degrees of freedom per grid. Hence, there is stiffness associated to each degree of freedom. In some finite element codes, shell elements do not have a drilling stiffness normal to the mid-plane, which may cause singular stiffness matrix. Then, a user-defined artificial stiffness value is assigned to this degree of freedom to avoid the singularity.

The second order shell elements (CTRIA6 and CQUAD8) have five degrees of freedom per grid. Rotational degrees of freedom without stiffness are removed through SPC.

Three-dimensional Solid Elements

Interface Elements

Interface elements are elements which are specialized for a particular purpose of simulating behavior at the interfaces between structures or on the surface of the structural elements interacting with the environment (for example, CHBDYE - thermal boundary surface elements, CIFPEN/CIFHEX - cohesive elements, and so on).

Offset for One-dimensional and Two-dimensional Elements

Some one-dimensional and two-dimensional elements can use offset to “shift” the element stiffness relative to the location determined by the element’s nodes. For example, shell elements can be offset from the plane defined by element nodes by means of ZOFFS. In this case, all other information, such as material matrices or fiber locations for the calculation of stresses, are given relative to the offset reference plane. Similarly, the results, such as shell element forces, are output on the offset reference plane.

Offset is applied to all element matrices (stiffness, mass, and geometric stiffness), and to respective element loads (such as gravity). Hence, in principle, offset can be used in all types of analysis and optimization.

However, caution is advised when interpreting the results, especially in linear buckling analysis. Without offset, a typical simple structure will bifurcate and loose stability “instantly” at the critical load. With offset, though, the loss of stability is gradual and asymptotically reaches a limit load, as shown in Figure 1(b):

Figure 1.

Furthermore, in a fully nonlinear approach, additional instability points may be present on the limit load path.

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