Verification of deforming polarized structure computation by using a closed-form solution

  • B. Emek Abali
  • Felix A. Reich
Original Article


Various engineering systems exploit the conversion between electromagnetic and mechanical work. It is important to compute this coupling accurately, and we present a method for solving the governing equations simultaneously (at once) without a staggering scheme. We briefly present the theory for coupling the elecgoverning equations as well as the variational formulation that leads to the weak form. This weak form is nonlinear and couples various fields. In order to solve the weak form, we use the finite element method in space and the finite difference method in time for the discretization of the computational domain. Numerical problems are circumvented by selecting the field equations carefully, and the weak form is assembled using standard shape functions. In order to examine the accuracy of the method, for the case of a linear elastic material under small deformations, we present and use an analytic solution. Comparison of the computation to the closed-form solution shows that the computational approach is reliable and models the jump of the electromagnetic fields across the interface between two different materials.


Mechanics Electromagnetism Finite element method 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Continuum Mechanics and Constitutive Theory, Institute of MechanicsTechnische Universität BerlinBerlinGermany

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