A geometrically nonlinear topology optimization design method for continuum structures based on a global solution strategy

Abstract

A geometric nonlinear topology optimization design method for a continuum structure based on a global solution strategy comprises the following steps: (1) establishing a base structure finite element model; (2) establishing an optimization model with the lightest structural mass as the goal and stress as the constraint condition; (3) setting the initial value of the topological variable and obtaining the base structure information; (4) performing a geometric nonlinear analysis on the structure and extracting the analysis results; (5) introducing a mass and unit stiffness filter function, and introducing a stress globalization constraint to realize the explicitness of the optimization model; (6) solving the optimization model using MMA to obtain an optimal continuous solution; (7) performing a discrete inversion on the optimal solution so that the structure satisfies the optimization criterion judgment, thereby obtaining an optimal topological structure. The present invention takes the geometric nonlinear response of the structure into consideration from the finite element analysis stage. The stress globalization calculation formula is introduced to obtain the strain energy constraint value, and the multi-constraint problem is converted into an extreme value problem, which reduces the amount of calculation and is of great significance for the design of engineering structures considering geometric nonlinearity.

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