On topology optimization of design-dependent pressure-loaded three-dimensional structures and compliant mechanisms

This paper presents a density-based topology optimization method for designing three-dimensional (3D) compliant mechanisms and loadbearing structures with design-dependent pressure loading. Instead of interface-tracking techniques, the Darcy law in conjunction with a drainage term is employed to obtain pressure field as a function of the design vector. To ensure continuous transition of pressure loads as the design evolves, the flow coefficient of a finite element is defined using a smooth Heaviside function. The obtained pressure field is converted into consistent nodal loads using a transformation matrix. The presented approach employs the standard finite element formulation and also, allows consistent and computationally inexpensive calculation of load sensitivities using the adjoint-variable method. For compliant mechanism design, a multi-criteria objective is minimized, whereas minimization of compliance is performed for designing loadbearing structures. Efficacy and robustness of the presented approach is demonstrated by designing various pressure-actuated 3D compliant mechanisms and structures.