Code Verification Examples of a Fully Geometrical Nonlinear Membrane Element using the Method of Manufactured Solutions

This paper presents an effective method to perform Code Verification of a software which is designed for structural analysis using membranes. The focus lies on initially curved structures with large deformations in steady and unsteady regimes. The material is assumed to be linear elastic isotropic. Code Verification is a part of efforts to guarantee the code’s correctness and to obtain finally predictive capability of the code. The Method of Manufactured Solutions turned out to be an effective tool to perform Code Verification, especially for initially curved structures. Here arbitrary invented geometries and analytical solutions are chosen. The computer code must approach this solution asymptotically. The observed error reduction with systematic mesh refinement (i.e. observed order of accuracy) must be in the range of the formal order of accuracy, e.g. derived by a Taylor series expansion. If these two orders match in the asymptotic range, the implemented numerical algorithms are working as intended. The given examples provide a complete hierarchical benchmark suite for the reader to assess other codes, too. In the present case several membrane states were tested successfully and the used code Carat++ assessed to converge as intended second order accurately in space and time for all kind of shapes and solutions.