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Dynamic behavior of thermoelastic solid continua using mathematical model derived based on non-classical continuum mechanics with internal rotations

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Abstract

This paper considers dynamic behavior of non-classical thermoelastic solid continua. The mathematical model consists of the conservation and balance laws of non-classical continuum mechanics that incorporates additional physics of internal rotations arising due to deformation gradient tensor. We consider plane stress behavior with small deformation, small strain physics only. Galerkin Method with Weak Form (GM/WF) in space is considered to construct a space–time decoupled finite element formulation giving rise to ordinary differential equations (ODEs) in time containing mass matrix, stiffness matrix due to classical as well as non-classical physics and acceleration and displacement associated with nodal degrees of freedom. This formulation is utilized to: (1) study natural undamped modes of vibration (2) study transient dynamic response by time integrating the ODEs in time (3) study the transient dynamic response by transforming the ODEs in time to modal basis using eigenvectors of the undamped natural modes. The ODEs in modal basis are used to construct transient dynamic response by time integrating them as well as by considering their analytical solutions. The solutions of the model problem obtained using the mathematical model based on non-classical continuum mechanics with internal rotations are presented and are compared with those obtained using the mathematical model based on classical continuum mechanics to demonstrate the influence of new physics due to internal rotations on the dynamic response of solid continua.

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Acknowledgements

First author is grateful for his endowed professorships and the department of mechanical engineering of the University of Kansas for providing financial support to the second author. The computational facilities provided by the Computational Mechanics Laboratory of the mechanical engineering department are also acknowledged.

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  1. Mechanical Engineering, University of Kansas, Lawrence, KS, USA

    K. S. Surana & C. H. Carranza

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  1. K. S. Surana
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  2. C. H. Carranza
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Correspondence to K. S. Surana.

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In honor of Professor J. N. Reddy for his 75th Birthday.

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Surana, K.S., Carranza, C.H. Dynamic behavior of thermoelastic solid continua using mathematical model derived based on non-classical continuum mechanics with internal rotations. Meccanica 56, 1345–1375 (2021). https://doi.org/10.1007/s11012-020-01221-2

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