Theoretical and experimental validation of the variable-thickness topology optimization approach for the rib-stiffened panels

In this paper, we consider compliance minimization problems within the variable-thickness approach for the rib-stiffened plates subjected to a transverse loading. It is known, that such optimization problems are usually not well posed and their solutions become strongly mesh-dependent. To overcome this issue, we introduce additional regularization constraint on the thickness gradient and evaluate the convergence and efficiency of considered method. Variable thickness is defined based on topology optimization approach introducing additional design variables in the nodes of the shell-type elements. Numerical solutions are provided by using finite element simulations within Mindlin-Reissner theory and method of moving asymptotes. Possibility for the well-converged optimal solutions for the benchmark problems with rib-stiffened panels loaded by the systems of concentrated forces is shown. Parametric studies are provided to analyse the effects of the shape functions order, values of penalty factors and initial conditions for the plate thickness. Recommendations for the optimal settings of the considered method are established. Theoretical and experimental assessments on the advantages and accuracy of the variable-thickness approach are given based on comparison of the obtained solutions to the standard design for the plates with regular stiffening.

Automated summary

This paper investigates the compliance minimization problems in rib-stiffened plates under transverse loading using the variable-thickness approach. The optimization problems in such cases are usually ill-posed and their solutions depend heavily on the mesh. To address this issue, an additional regularization constraint is introduced on the thickness gradient, and the convergence and efficiency of the method are evaluated. Variable thickness is defined using a topology optimization approach, introducing additional design variables in the nodes of shell-type elements. Numerical solutions are obtained through finite element simulations using Mindlin-Reissner theory and the method of moving asymptotes. The study shows that well-converged optimal solutions can be achieved for benchmark problems with rib-stiffened panels loaded by concentrated forces. Parametric studies are conducted to analyze the effects of shape function order, penalty factor values, and initial conditions for plate thickness. Recommendations for optimal settings of the method are established, and theoretical and experimental assessments on the advantages and accuracy of the variable-thickness approach are provided based on comparisons with standard designs.