A parallel finite-element framework for large-scale gradient-based design optimization of high-performance structures

• Structural optimization: Gradient evaluation is the computational bottleneck.
• Gradient evaluation technique scales with processors, functions, and design variables.
• Computational time of parallel matrix factorization independent of element order.
• Verification case proposed for optimization testing solution/functional accuracy.

Structural optimization using gradient-based methods is a powerful design technique that is well suited for the design of high-performance structures. However, the ever-increasing complexity of finite-element models and design formulations results in a bottleneck in the computation of the gradients required for the design optimization. Furthermore, in light of current high-performance computing trends, any methods intended to address this bottleneck must efficiently utilize parallel computing resources. Therefore, there is a need for solution and gradient evaluation methods that scale well with the number of design variables, constraints, and processors. We address this need by developing an integrated parallel finite-element analysis tool for gradient-based design optimization that is designed to use specialized parallel solution methods to solve large-scale high-fidelity structural optimization problems with thousands of design variables, millions of state variables, and hundreds of load cases. We describe the most relevant details of the parallel algorithms used within the tool. We present consistent constraint formulations and aggregation techniques for both material failure and buckling constraints. To demonstrate both the solution and functional accuracy, we compare our results to an exact solution of a pressure-loaded cylinder made with either isotropic or orthotropic material. To demonstrate the parallel solution and gradient evaluation performance, we perform a structural analysis and gradient evaluation for a large transport aircraft wing with over 5.44 million unknowns. The results show near-ideal scalability of the structural solution and gradient computation with the number of design variables, constraints, and processors, which makes this framework well suited for large-scale high-fidelity structural design optimization.