Abstract
Geometric nonlinear solution of a compressed plate is presented in this paper. Basic assumptions are specified and incremental conditional equations are derived from the variational principle of minimum of total potential energy. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied for solution. The importance of modifications of base functions for solving geometric nonlinear problems is analysed. The solved example is presented, the differences are compared and explained.
Highlights
Thin rectangular plates are the simplest shapes, easy to made they are widely used in many branches of engineering
The solution of the system (5) cannot be achieved directly, and is based on a step by step incremental process that causes a deviation from the equilibrium nonlinear path
Presented results have been arranged due to the research supported by the Slovak Scientific Grant Agency, project No 1/0265/16
Summary
Thin rectangular plates are the simplest shapes, easy to made they are widely used in many branches of engineering. Stored strain energy can be suddenly released and converted into kinetic energy with subsequent collapse of the structure. It is the reason why the stability problem has been analyzed since the beginning of the twenty century. In this paper the effect of choice of base functions upon the mesh density of thin plate structures as well as upon the convergence of FEM solution of stability problems, have been studied. Numerical analysis of stability problems has been converging from above, the mesh density should be identified at which the obtained results are applicable.
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