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The incompressible von Kármán theory for thin prestrained plates

Hui Li

Abstract

We derive a new version of the von Kármán energy and the corresponding Euler-Langrange equations, in the context of thin prestrained plates, under the condition of incompressibility relative to the given prestrain. Our derivation uses the theory of $Γ$-convergence in the calculus of variations, building on prior techniques in [Conti, Dolzmann (2009)] and [Lewicka, Mahadevan, Pakzad (2011)].

The incompressible von Kármán theory for thin prestrained plates

Abstract

We derive a new version of the von Kármán energy and the corresponding Euler-Langrange equations, in the context of thin prestrained plates, under the condition of incompressibility relative to the given prestrain. Our derivation uses the theory of -convergence in the calculus of variations, building on prior techniques in [Conti, Dolzmann (2009)] and [Lewicka, Mahadevan, Pakzad (2011)].

Paper Structure

This paper contains 5 sections, 4 theorems, 74 equations.

Table of Contents

  1. Introduction
  2. Statements of the main results
  3. Compactness and the lower bound
  4. Construction of the recovery sequence
  5. The Euler-Lagrange Equations for prestrained isotropic thin plates

Key Result

Theorem 2.1

Theorems & Definitions (6)

  • Theorem 2.1
  • Theorem 3.1
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • proof