Frequency-constrained topology optimization in incompressible multi-material systems under design-dependent loads

Abstract

In the realm of engineering design, structures grappling with fluidic pressure loads within precise frequency constraints necessitate innovative approaches. This study introduces a method to address the intricacies of design-dependent load-based structures, focusing on three key aspects: (i) managing structures constrained by frequency under fluidic pressure loads dependent on the design, (ii) integrating the use of multiple materials, and (iii) dealing with nearly incompressible materials. The proposed approach, detailed in this paper, employs polytopal composite finite elements (PCEs) to overcome the inherent volumetric locking phenomenon in incompressible materials. By incorporating Darcy’s law and a drainage term alongside the representative-solid phase, this approach ensures consistent treatment of fluidic pressure loads, dynamically adjusting their direction and location during the multi-material design process. The porosity of each element, intricately linked to its density variable through a Heaviside function, facilitates a smooth transition between solid and void phases. The application of Darcy’s law establishes a specific pressure field, solved using PCEs, enabling the computation of consistent nodal loads. This method simplifies the assessment of load sensitivities through the adjoint-variable technique. The method’s effectiveness and reliability are validated through numerical examples, demonstrating its capability to optimize compliance within specific volume constraints for frequency-limited structures subjected to design-dependent pressure loading and considering a diverse range of materials from compressible to nearly incompressible.