Modification of the Finite-Element Method to Apply to Problems of the Equilibrium of Bodies Subject to Large Deformations

The analytical expressions for the elements of the Jacobian matrix of the tensor-matrix system of FEM equations that describes the large deformations of an incompressible elastic body are derived using derivatives with respect to a tensor argument. The results are obtained for the general three-dimensional case, including the case of plane strain. The stress–strain state of a hollow square prism turned inside out is determined with a numerical method using the Jacobian matrix

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Correspondence to V. V. Chekhov.

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Translated from Prikladnaya Mekhanika, Vol. 49, No. 6, pp. 37–43, November–December 2013.

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Chekhov, V.V. Modification of the Finite-Element Method to Apply to Problems of the Equilibrium of Bodies Subject to Large Deformations. Int Appl Mech 49, 658–664 (2013). https://doi.org/10.1007/s10778-013-0599-1

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Keywords

  • finite-element method
  • tensor-matrix system of equations
  • large deformations
  • Finger strain measure
  • incompressible elastic body
  • tensor derivative
  • Jacobian matrix
  • hollow square prism turned inside out