About element verification tests

This set includes two tests for most element types. In the first of these tests all the modes and frequencies of a single, unrestrained element are extracted. The second test extracts the modes and frequencies of a patch of unrestrained elements. These tests verify the correct representation of rigid body modes and the correctness of each element's stiffness and mass. The tests also reveal any singular “hourglass” modes that may be present in reduced-integration elements.

A third test is performed to extract the natural modes of vibration of an organ pipe modeled with acoustic elements.

Only the number of zero-energy modes has been verified for the tests. The first nonzero eigenvalue is shown only for purposes of comparison. These tests are not performed for heat transfer elements and some other nonstructural elements.

In these tests a simple domain, such as a rectangle in two dimensions or a rectangular prism in three dimensions, is discretized with the minimum number of elements. Sufficient kinematic boundary conditions are imposed to remove rigid body motion only. The loadings that are applied are ones for which the element being tested is capable of representing the solution exactly; for example, first-order elements are loaded so as to cause a constant stress state, while second-order elements are loaded into a linearly varying stress state. The results are checked against exact calculations.

Several such tests are necessary for structural elements (beams and shells) because of their complexity, and different tests are used for the elements that are based on the Kirchhoff hypothesis and for those that provide shear flexibility. The tests also include discontinuous structures (plates joined at an angle and frames) to test defining discontinuous normals, and they include shells and membranes with variable thickness. The local coordinate definitions are verified in some tests.

The problem descriptions contain the solution with which the results are compared. Where analytical solutions are not available, alternative numerical solutions are used.

In these tests the distributed loadings provided for each element are verified by checking the equivalent nodal forces, fluxes, or charges that are calculated for each load type. All degrees of freedom are suppressed, and the various distributed loadings offered for the element type are applied in a series of steps. The reactions are verified against exact calculation for the interpolation function. The values of the output variables presented are “exact” in the finite element sense and, unless noted otherwise, are also exact in the analytical sense.

To check thermal loading, free and constrained thermal expansions of elements are also tested. Thermal loads are defined by giving the temperature, $\theta$, along with a nonzero thermal expansion coefficient.

Generalized plane strain elements have an additional reference node associated with the generalized plane strain condition. Depending on the particular test, degrees of freedom $u_z$, ${\varphi }_x$, and ${\varphi }_y$ of the generalized plane strain reference node are constrained or left free.

The patch test requires that, for an arbitrary “patch” of elements, when a solution corresponding to a state of constant strain throughout the patch is prescribed on the boundary of the patch, the constant strain state must be obtained as the solution at all strain calculation points throughout the patch. For heat transfer elements the patch test requires that constant temperature gradients are calculated throughout the patch when the temperatures corresponding to the constant gradient solution are prescribed on the boundary. The acoustic elements are similarly tested for constant pressure gradients, and the thermal-electrical elements are tested for constant potential gradients.

The patch test is generally considered to be a necessary and sufficient condition for convergence of the solution as the element size is reduced, except for shell elements of the type used in Abaqus, for which the test is not rigorously required, but for which it is commonly accepted as a valuable indicator of the element's quality. Thus, this test plays a key role in the verification process.

In the patch tests done in Abaqus a patch is defined as a mesh with at least one interior element and several interior nodes. The elements in the patch are nonrectangular, although element edges are kept straight. (Second-order elements do not always pass the patch test if their edges are not straight.) The shell elements are tested for plate and cylindrical patches only.

Basic verification of the geometric nonlinearity capability is included in these tests by prescribing large rigid body rotations of the models under states of constant strain and verifying the invariance of the solution with respect to the rotation.

This section contains tests of the various contact capabilities available in Abaqus.

This section contains tests of the various interface capabilities available in Abaqus. This category currently consists of modeling surface interface conditions in heat transfer problems, coupled acoustic-structural problems, coupled thermal-electrical problems, and friction.

This section contains tests of the rigid body elements available in Abaqus/Explicit.

This section contains tests of the connector elements available in Abaqus.

This section describes tests of some of the special-purpose stress/displacement elements available in Abaqus that are not tested in other sections of this guide. SPRING- and MASS-type elements are tested with the eigenvalue frequency analyses of Eigenvalue extraction for single unconstrained elements. ELBOW-type elements are also tested in Eigenvalue extraction for single unconstrained elements, as well as in the simple load test described in Verification of beam elements and section types and the distributed load test described in ELBOW elements. GAP-type elements are tested with the contact elements, as described in Contact between discrete points.

This category contains tests of the rebar options, transport of a temperature pulse in convection elements, transverse shear for shear-flexible shells, and linear dynamic analyses with fluid link elements.