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

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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.