  Shape optimization is of great significance in structural engineering, as an
efficient geometry leads to better performance of structures. However, the
application of gradient-based shape optimization for structural and
architectural design is limited, which is partly due to the difficulty and the
complexity in gradient evaluation. In this work, an efficient framework based
on automatic differentiation (AD), the adjoint method and accelerated linear
algebra (XLA) is proposed to promote the implementation of gradient-based shape
optimization. The framework is realized by the implementation of the
high-performance computing (HPC) library JAX. We leverage AD for gradient
evaluation in the sensitivity analysis stage. Compared to numerical
differentiation, AD is more accurate; compared to analytical and symbolic
differentiation, AD is more efficient and easier to apply. In addition, the
adjoint method is used to reduce the complexity of computation of the
sensitivity. The XLA feature is exploited by an efficient programming
architecture that we proposed, which can boost gradient evaluation. The
proposed framework also supports hardware acceleration such as GPUs. The
framework is applied to the form finding of arches and different free-form
gridshells: gridshell inspired by Mannheim Multihalle, four-point supported
gridshell, and canopy-like structures. Two geometric descriptive methods are
used: non-parametric and parametric description via B\'ezier surface.
Non-constrained and constrained shape optimization problems are considered,
where the former is solved by gradient descent and the latter is solved by
sequential quadratic programming (SQP). Through these examples, the proposed
framework is shown to be able to provide structural engineers with a more
efficient tool for shape optimization, enabling better design for the built
environment.
