Keywords: finite elements, multiphysics, wave propagations, shells, large strains, improvements of stresses, Maxwell's equations, electromechanics, fluid flows.

The analysis of solids and structures in multiphysics conditions has been given increasing attention during the recent years. A large number of problems considered only a decade ago as very difficult to solve can now be analyzed with relatively little computational effort. However, there are many problem areas where significant advances are still needed for effective simulations.

The objective in this presentation is to summarize our research efforts to advance the state of computational simulations in engineering and the sciences. We present our recent developments regarding the analysis of transient and wave propagation problems [1-3], the analysis of shells [4-6], the prediction of more accurate stresses [7], the use of interpolation covers to increase the convergence of solutions [8], and the coupling of structures to general fluid flows and electromagnetic effects [9].

The field of multiphysics is very large and we must expect that multiphysics problems will be tackled to an increasing extent: in engineering, where new designs require a deeper understanding of performances, see e.g. [10, 11], and in the sciences, because a deeper understanding of nature through simulations will create important advances – for example, in the field of medical sciences in particular.

[1]

S. Ham, K.J. Bathe, "A Finite Element Method Enriched for Wave Propagation Problems", Comput. & Struct., 94-95, 1-12, 2012. doi:10.1016/j.compstruc.2012.01.001

[2]

K.J. Bathe, G. Noh, "Insight into an Implicit Time Integration Scheme for Structural Dynamics", Comput. & Struct., 98-99, 1-6, 2012. doi:10.1016/j.compstruc.2012.01.009

[3]

Z. Kazanci, K.J. Bathe, "Crushing and Crashing of Tubes with Implicit Time Integration", Int. J. Impact Engineering, 42, 80-88, 2012. doi:10.1016/j.ijimpeng.2011.10.003

[4]

K.J. Bathe, P.S. Lee, "Measuring the Convergence Behavior of Shell Analysis Schemes", Comput. & Struct., 89, 285-301, 2011. doi:10.1016/j.compstruc.2010.09.007

[5]

D. Chapelle, K.J. Bathe, "The Finite Element Analysis of Shells – Fundamentals", Springer, first edition 2003, second edition 2011. doi:10.1007/978-3-642-16408-8

[6]

T. Sussman, K.J. Bathe, "3D-Shell Elements for Structures in Large Strains", in preparation.

[7]

D.J. Payen, K.J. Bathe, "A Stress Improvement Procedure", Comput. & Struct., submitted.

[8]

J. Kim, K.J. Bathe, "The Finite Element Method Enriched by Interpolation Covers", in preparation.

[9]

K.J. Bathe, H. Zhang, Y. Yan, "The Solution of Maxwell’s Equations in Multiphysics", in preparation.

[10]

C. Deilmann, K.J. Bathe, "A Holistic Method to Design an Optimized Energy Scenario and Quantitatively Evaluate Promising Technologies for Implementation", International Journal of Green Energy, 6, 1-21, 2009. doi:10.1080/15435070802701702

[11]

M.L. Bucalem, K.J. Bathe, "The Mechanics of Solids and Structures – Hierarchical Modeling and the Finite Element Solution", Springer, 2011. doi:10.1007/978-3-540-26400-2

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