座屈に対する形状最適化

抄録

A shape optimization method for linear buckling load maximization problems of continua is presented. Using a one-parameter family of mappings defined in a domain where a continuum lies initially, a buckling load maximization problem considering multimodal conditions was formulated. The shape gradient density function for the problem was derived using the Lagrange multiplier method and the formula of the material derivative. The shape gradient density function was then used in a shape optimization analysis conducted with the traction method. The validity of the proposed method was demonstrated by numerical analyses of column-like and arch-like two-dimensional continua in a plane strain condition.