Vertex assigned morphing for parameter free shape optimization of 3-dimensional solid structures

In the past the Vertex Morphing method has mainly been used in the context of optimization of thin walled shell structures or fluid mechanical problems. In this paper an extension of this parameter free shape optimization method to 3-dimensional solid structures based on the free Finite Element code CalculiX is presented. Key element of the whole process is an efficient adjoint sensitivity analysis that can handle many design variables providing gradient information for the response functions of interest, e.g. stresses and mass. Typically, parameter free shape optimal designs result in non-smooth geometries and suffer from mesh dependencies. To avoid these phenomena an intermediate filter operation in combination with several post processing steps of the raw sensitivities is added. In the optimization, the filter size is also used as an additional design parameter controlling the curvature of the optimal shape. In many engineering optimization applications constraints have to be considered. These restrictions are included in the optimization problem by the use of Rosen’s gradient projection method. For the successive shape update a pseudo linear-elastic static Finite Element analysis with multiple point constraints and a varying Young’s modulus is performed in every design iteration. Finally, the capabilities of the extended Vertex Morphing method are demonstrated for an academic example and a geometrically complex part from aerospace industry. •A gradient-based, parameter free shape optimization method for 3-dimensional solid structures based on the FE-software CalculiX is presented.•Sensitivities are based on an adjoint formulation with an intermediate filter step.•Constraints, e.g. mass of the structure, are taken into account by the gradient projection method.•For the mesh update a pseudo linear equation system is solved with multiple point constraints and a varying Young’s modulus gaining a higher level of flexibility w.r.t. the shape change.•The capabilities of the whole optimization process are demonstrated on a geometrically complex part from aerospace industry.