A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Green and Lindsay’s dynamic thermoelasticity model is selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. Time integration of the semidiscrete finite element equations is achieved by using an implicit-explicit scheme proposed by Hughes, et al. The procedure proves to be most effective and versatile in thermal and stress wave propagation analysis. A number of examples are presented which demonstrate the accuracy and versatility of the proposed model, and the importance of finite thermal propagation speed effects.
We show that the only real symmetric matrices whose spectrum is invariant modulo sign changes after either row or column reversal are the centrosymmetric matrices; moreover, we prove that the class of real symmetric centrosymmetric matrices can be completely characterized by this property. We also show that the only real symmetric matrices whose spectrum changes by multiplication by i after either row or column reversal are the skew-centrosymmetric matrices; here, too, we show that the class of real symmetric skew-centrosymmetric matrices can be completely characterized by this property of their eigenvalues. We prove both of these spectral characterizations as special cases of results for what we've called generalized centrosymmetric K-matrices and generalized skew-centrosymmetric K-matrices. Some results illustrating the application of the generalized centrosymmetric spectral characterization to other classes of real symmetric matrices are also given.
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