Aspects of thermally induced buckling of patched structures

A review, unification and extension of analysis and results of patched beam-plates subjected to a uniform temperature field is presented where both heating and cooling is considered. The self-consistent non-linear formulation lends itself to an exact analytical solution, to within a numerically determined parameter. Stability is assessed by examination of the second variation of the energy functional along the loading path. Three non-dimensional parameters are seen to characterize the response of the composite system. These are (i) a loading parameter, (ii) a critical temperature, and (iii) a critical membrane force. Critical behavior includes asymptotic buckling, bifurcation and snap-through buckling, non-trivial 'ground states', and demarcation and transition in deflection direction. Extensive numerical simulations based on analytical solutions elucidate the intricate, and sometimes unexpected behavior, and the factors that control such behavior.