A Nonlinear Programming Paradigm for Hybrid Elements Formulation Towards High-Performance Collapse Simulations

在包括结构倒塌分析在内的各种工程模拟中，非线性效应的考虑是必不可少的。各种结构体系在极端荷载下表现出重要的几何和材料非线性，对结构性能的现实评估迫使研究人员、工程实践和建筑规范求助于日益复杂的非线性分析方法。因此，对非线性现象的准确和计算效率的评估对于增强安全性的可持续结构设计至关重要。因此，现代结构分析工作的重点是估计结构破坏和性能，直至倒塌。可靠地预测结构系统的行为，直到其倒塌，具有重大的经济和生命安全意义。这项研究的主要目的是绕过坍塌和高度非线性模拟中出现的几个缺陷，并提高结构分析困难问题的质量、效率和精度。除了在结构工程问题的数值分析方面取得的重要科学进展，以及与改进结构设计、更安全的结构和有效的失效预测有关的社会和经济效益外，这项研究还可以为更广泛的学术领域做出贡献。类似的大弹性和非弹性位移现象在多个科学领域和应用中具有特殊的意义，因此研究成果可以帮助解决许多领域的相关计算问题。所使用的精确运动学表达式是实现高性能坍塌模拟的基本属性，即允许精度、粗离散化、计算速度、算法稳健性和无锁定单元，即使在非常大的非弹性位移的情况下也是如此。为了实现这些目标，总势能泛函将通过拉格朗日乘子进行杂交，以确保兼容性，并将在每个元素的配置点进行评估。这一过程产生了梁柱混合有限元，而结构分析则被表述为一个纯粹的非线性规划问题，寻求能量方面的最优。这一概念开启了一条全新的研究道路，具有超越传统线性化方案的潜力，并将非线性结构分析的哲学与非线性规划概念和该领域丰富的复杂方法相结合。总体而言，这一研究项目将提高倒塌模拟的质量，将促进改进的和物理上一致的损伤极限状态定义，将提出新的科学和计算范式，并将在要求苛刻和计算密集的大型结构问题中推动计算效率的极限。

In a great variety of engineering simulations, including structural collapse analysis, consideration of nonlinear effects is indispensable. Various structural systems exhibit important nonlinearities under extreme loads, both in terms of geometry and material, and a realistic evaluation of structural behavior has been forcing researchers, engineering practice and building codes to resort to increasingly sophisticated nonlinear analysis approaches. Accurate and computationally efficient assessment of nonlinear phenomena is hence of vital importance towards sustainable structural designs of enhanced safety. Modern structural analysis efforts focus therefore in estimating structural damage and performance all the way up to collapse. Reliably predicting the behavior of a structural system until its collapse has significant economic and life safety implications. The main objectives of this research is to circumvent several deficiencies emerging in collapse and highly nonlinear simulations and to upgrade the quality, efficiency and accuracy of difficult structural analysis problems. Apart from the important scientific advancements in numerical analysis of structural engineering problems and the societal and economic benefits in relation to improved structural design, safer structures and effective failure predictions, this research can also contribute to a much wider academic spectrum. Similar phenomena of large elastic and inelastic displacements are of particular interest in multiple scientific fields and applications, and research outcomes can thus help the solution of related computational problems in numerous areas.An original hybrid element formulation based on a new nonlinear programming paradigm will be studied in this research. The exact kinematic expressions used are the essential properties that enable high-performance collapse simulations, namely allow for accuracy, coarse discretization, computational speed, algorithmic robustness and locking-free elements, even with very large inelastic displacements. Towards these goals, the total potential energy functional will be hybridized through Lagrange multipliers that assure compatibility and will be evaluated at collocation points within each element. This procedure results to a hybrid beam-column finite element, whereas structural analysis is formulated and treated as a pure nonlinear programming problem, seeking optima in terms of energy. This concept unlocks an entirely new research path, having the potential to outperform conventional linearization schemes and integrating the philosophy of nonlinear structural analysis with nonlinear programming concepts and the abundance of sophisticated methods in the field. Overall, this research project will advance the quality of collapse simulations, will facilitate improved and physically consistent damage limit state definitions, will pose new scientific and computational paradigms, and will push the limits of computational efficacy in demanding and computationally intensive large scale structural problems.