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Analytical and numerical tests for loss of material stability. (English) Zbl 0895.73028

We provide an analytical development for loss of ellipticity together with an explicit expression for the normal to the bifurcation plane. Numerical solutions are given for several sample problems. For all cases, the numerical solutions based on the finite element method conform to the theoretical expectations that a unique numerical solution exists prior to the point at which ellipticity is lost.

MSC:

74G99 Equilibrium (steady-state) problems in solid mechanics
74H99 Dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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