关键词: 屈曲, 有限元法, 非均匀分布载荷, 矩形板

Abstract: Linear buckling problems of rectangular plates subjected to in-plane compressive loadings have been researched for many years. Theory has been relatively mature and there are manuals for designers to consult. Since analytical solutions for the plate subjected to non-uniformly distributed loading are not easy to obtain, in obtaining the buckling load, the distributions of the in-plane stresses are usually assumed as the same as the loads applied on the edges. Actually the distribution of the in-plane stresses is quite different from the assumption. Moreover, other two stress components also appear and their effects on the buckling load depend on the boundary conditions. Finite element method is used to investigate the buckling behaviors of thin plates subjected to non-uniformly distributed loadings. The buckling loads for several boundary conditions are given. For convenience to the designers, formulae are given to relate the buckling loads subjected to non-uniformly distributed loads with these subjected to equivalent uniformly distributed loads. It is found that some buckling loads listed in the "Aircraft Design Manual" are inaccurate for one case of plates subjected to linearly distributed loadings. The present results may provide a reference for designing plate structures subjected to non-uniformly distributed loadings.

Key words: buckling, FEM, non-uniformly distributed load, rectangular plate