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Matrix Mechanics to Classify Non-Linear Continua

In: Numerical Techniques for Engineering Analysis and Design

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  • J. D. Coleman

    (The City University, Senior Visiting Fellow Fluid Mechanics Division Department of Civil Engineering)

Abstract

Summary Matrix Mechanics is a procedure to classify linear, semi-linear and quasi-linear continua from the system of E first order partial differential equations in E dependent variables which define them. Purpose is to index problems, seek analogues and determine boundary conditions for higher order systems. The type assists choice of stable,efficient and convergent numerical procedures for the continuum. Dummy variables are used to reduce any second order terms to first order-one more variable-one more equation.System is arranged with each dependent variable in vertical rows. Each ux say is replaced by Cx etc., where C(x y z t)=const. is a characteristic for the system.The equation det A=0 then defines all the E characteristics.The paper gives ground rules for determining characteristic classes. Then examples are systematically presented in eight different selected classes.

Suggested Citation

  • J. D. Coleman, 1987. "Matrix Mechanics to Classify Non-Linear Continua," Springer Books, in: G. N. Pande & J. Middleton (ed.), Numerical Techniques for Engineering Analysis and Design, chapter 0, pages 135-142, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3653-9_16
    DOI: 10.1007/978-94-009-3653-9_16
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