Steady-State Problems of Nonlinear Electro-Magneto-Thermo-Elasticity.

Abstract

This paper studies the steady-state behavior of solids that can sustain mechanical, electromagnetic, and thermal effects. The authors examine a class of boundary-value problems for a quasilinear system of functional differential equations that is derived from a very general model for such materials. They propose a physically reasonable constitutive theory which leaves this system amenable to modern methods of partial differential equations. The principal assumption is a modified version of the strong ellipticity condition. Part I proves existence results for the general system under some special physical assumptions (rigidity and hyperelasticity). The formulation admits non-local interactions caused by the magnetic 'self-field' generated by the deformed, conducting body. Part II shows the existence and regularity of solutions of a system of functional ordinary differential equations arising from a semi-inverse problem in a more comprehensive physical situation. Keywords: Smooth solutions; Polyconvex energy functions; Electro-elastic coupling; Magneto-elastic coupling; Conducting rods; Thermo-elastic coupling. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1986
Accession Number
ADA167454

Entities

People

  • Robert C. Rogers
  • Stuart S. Antman

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Advanced Electronics
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Computational Science
  • Constitutive Equations
  • Differential Equations
  • Electromagnetic Fields
  • Electromagnetism
  • Equations
  • Inverse Problems
  • Magnetic Fields
  • Materials
  • Mathematical Analysis
  • Mathematics
  • Mechanics
  • Partial Differential Equations
  • Steady State
  • Temperature Gradients
  • United States

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Plasma Physics / Magnetohydrodynamics
  • Systems Analysis and Design

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  • AI & ML
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