Efficient non‐linear finite element shell formulation involving large strains

Abstract

A previously presented finite element shell formulation is extended to the application of large strains. The finite elements are those based on the concept of ‘the degenerated solids’, which are widely used in non‐linear finite element programs. The constitutive equation of hyperelastic incompressible material is adopted and specialized to the Mooney‐Rivlin law. The additional state variable, the hydrostatic pressure, which occurs for incompressible materials, is eliminated on element level using the plane stress condition. Attention is drawn to the efficient calculation of the element matrices by applying a layer concept. The effectiveness of the proposed total Lagrangian formulation is demonstrated in a number of example problems.

Citation

Parisch, H. (1986), "Efficient non‐linear finite element shell formulation involving large strains", Engineering Computations, Vol. 3 No. 2, pp. 121-128. https://doi.org/10.1108/eb023650