Finite element formulations for large deformation dynamic analysis

Abstract

SUMMARYStarting from continuum mechanics principles, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non-linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber-like) and hypoelastic elastic-plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.

Dynamic response of functionally graded skew shell panel

“…The first part gives deep insight about the vibration characteristics of various forms of functionally graded skew shells (cylindrical, spherical and hypar) by incorporating different parameters such as skew angle (α), thickness ratio (a/h), curvature ratio (R/a) and boundary conditions (simply supported and clamped). In the second part, dynamic response of skew shell is performed using Newmark integration scheme [16]. It is anticipated that the present results paves the way for researchers who are involved in the area of functionally graded skew shells.…”

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Salt tectonics as a self‐organizing process: A reaction, transport, and mechanics model

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Some practical procedures for the solution of nonlinear finite element equations

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