FDMopt: Force density method for optimal geometry and topology of trusses

Abstract

This paper presents a new efficient tool for simultaneous optimization of topology and geometry of truss structures. Force density method is applied to formulate optimization problem to minimize compliance under constraint on total structural volume, and objective and constraint functions are expressed as explicit functions of force density only. This method does not need constraints on nodal locations to avoid coalescent nodes, and enables to generate optimal solutions with a variety in topology and geometry. Furthermore, for the purpose of controlling optimal shapes, tensor product Bézier surface is introduced as a design surface. The optimization problem is solved using sensitivity coefficients and the optimizer is compiled as a component compatible with Grasshopper, an algorithmic modeling plug-in for Rhinoceros, which is a popular 3D modeling software. Efficiency and accuracy of the proposed method are demonstrated through two numerical examples of semi-cylindrical and semi-spherical models.