Abstract We present an optimal shape design problem of a transversely and axially loaded nonlinear stepped elastic beam with piecewise constant thickness distribution. The nonlinear beam model proposed by D.Y. Gao in 1996 is considered for modelling the state problem. The objective of the optimization is to find the thickness distribution to maximize the stiffness of the beam subjected to geometrical constraints, namely the preservation of volume is imposed. The stiffness is characterized by the compliance cost functional. The existence of solutions of the optimization problem and convergence properties of discretization using finite element approach is analysed. The theory is illustrated by numerical results.

中文翻译：

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阶梯非线性高梁的最佳厚度分布

摘要 我们提出了具有分段恒定厚度分布的横向和轴向加载非线性阶梯弹性梁的优化形状设计问题。DY Gao 在 1996 年提出的非线性梁模型被考虑用于建模状态问题。优化的目标是找到厚度分布以最大化受到几何约束的梁的刚度，即强加了体积保持。刚度以合规成本函数为特征。分析了优化问题解的存在性和有限元离散化的收敛性。数值结果说明了该理论。