Large thermoelastic deflections and stability of simply supported polygonal panels
A Berger-type approximation for large deflections of thermally loaded initially curved elastic plates is derived. In case of simply supported boundaries and arbitrary polygonal planforms, dimensionless solution is found in terms of Dirichlet's Helmholtz-eigenvalues of the given domain. Stability of this equilibrium solution is exemplarily discussed, showing bifurcation and snapping behaviour in the sense of a cusp catastrophe. Additionally, possibility of mode-jumping is indicated.
second order Helmholtz-Klein- Gordon boundary value problem
homogeneous Dirichlet boundary conditions
nonlinear algebraic equation for Berger's hydrostatic in-plane force
scientific article; zbMATH DE number 3930466
scientific article