A finite-variation method in nonlinear shell mechanics
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A numerical algorithm is proposed for calculating coefficients of first-and second-order variations of strain energy in a nonlinear finite-element model of a shell, which are necessary to define equilibrium states of the shell and investigate stability of the states. Several numerical schemes are considered based on various finite-difference approximations. For these schemes, the accuracy, convergence, and computation time are analyzed using popular geometrically nonlinear problems of deformation of elastic plates and shells.
Key wordsfinite-variation method thin shell large displacements strain energy finite element
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