Size, shape and topology optimization of truss structure via the finite particle method

The finite particle method (FPM), a novel numerical analysis approach for simulating structural statics and dynamics, is introduced into the field of structural optimization through the development of a new structural sensitivity analysis procedure. Using FPM, we can analyze static and dynamic structural responses, including typical nonlinear behaviors, based on a system composed of a finite number of particles. The new sensitivity analysis procedure integrates seamlessly with the general time-difference scheme of FPM. In the initial application of this sensitivity analysis procedure, we focus on the static optimization of truss structures. Optimization strategies tailored to truss structures are developed by predicting static responses via FPM. The positions of improperly placed particles are adjusted through particle fusion and projection strategies to achieve a reasonable configuration, enabling collaborative size, shape, and topology optimization. Various 2D and 3D numerical examples demonstrate the effectiveness and efficiency of the static optimization framework, made possible by the new sensitivity analysis procedure and FPM.