This paper describes an inverse shape design method for thermoelastic bodies. With a known equilibrium shape as input, the focus of this paper is the determination of the corresponding initial shape of a body undergoing thermal expansion or contraction, as well as nonlinear elastic deformations. A distinguishing feature of the described method lies in its capability to approximately prescribe an initial heterogeneous temperature distribution as well as an initial stress field even though the initial shape is unknown. At the core of the method, there is a system of nonlinear partial differential equations. They are discretized and solved with the finite element method or isogeometric analysis. In order to better integrate the method with application-oriented simulations, an iterative procedure is described that allows fine-tuning of the results. The method was motivated by an inverse cavity design problem in injection molding applications. Its use in this field is specifically highlighted, but the general description is kept independent of the application to simplify its adaptation to a wider range of use cases.

中文翻译：

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基于非线性热弹性材料模型的逆向设计应用于注塑成型

本文介绍了一种热弹性体的逆向形状设计方法。以已知的平衡形状作为输入，本文的重点是确定经历热膨胀或收缩以及非线性弹性变形的物体的相应初始形状。所描述的方法的一个显着特征在于它能够近似地规定初始异质温度分布以及初始应力场，即使初始形状未知。该方法的核心是一个非线性偏微分方程组。它们被离散化并用有限元方法或等几何分析求解。为了更好地将该方法与面向应用的模拟相结合，描述了一个迭代过程，允许对结果进行微调。该方法是由注塑成型应用中的反向型腔设计问题推动的。它在该领域的使用被特别强调，但一般描述保持独立于应用程序，以简化其对更广泛用例的适应。