AI 中文总结
本文提出将非线性耗散不等式作为连续介质力学约束方程的求解方法，通过凸优化问题处理杆件弹塑性响应的约束优化，可自动修正错误本构设定，使解符合力学基本假设。
AI 中文摘要
本文提出一种求解方法，将非线性耗散不等式作为连续介质力学中的约束方程处理，同时允许本构行为的知识不完整。该方案在杆件率相关弹塑性响应的背景下得到验证，形成一个非线性约束优化问题。研究得到了闭式解和计算结果，计算解利用一系列凸优化问题，且被证明是准确的。在示例中，该方法可自动修正（故意设置的）错误本构设定，使解符合连续介质力学的基本假设。
英文摘要
A solution procedure is formulated and solved for treating the nonlinear Dissipation Inequality as a constraint equation within continuum mechanics, and allowing for incomplete knowledge of constitutive behavior. The scheme is demonstrated in the context of the rate-dependent, elastoplastic response of a bar, resulting in a nonlinear problem of constrained optimization. Both closed form and computational results are developed. The computational solutions utilize a sequence of convex optimization problems, and are shown to be accurate. In the example considered, the approach is shown to automatically correct an (intentionally) faulty constitutive specification, resulting in the solution to be in accord with the fundamental postulates of continuum mechanics.
Comments16 pages, 10 figures
