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Continuous and discontinuous finite element approximations of shock waves in nonlinear elastic solids

Lectures

Part of the Lecture Notes in Mathematics book series (LNM,volume 461)

Keywords

  • Shock Wave
  • Shock Surface
  • Lagrange Formula
  • Finite Element Analogue
  • Explicit Finite Difference Scheme

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References

  1. J. T. Oden, Finite Elements of Nonlinear Continua, McGraw-Hill, N.Y. 1972.

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  2. J. T. Oden, Approximations and Numerical Analysis of Finite Deformations of Elastic Solids, Nonlinear Elasticity, Academic Press, N.Y., 1973, pp. 175–228.

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  3. J. T. Oden, Formulation and Application of Certain Primal and Mixed Finite Element Models of Finite Deformations of Elastic Bodies.

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  4. R. B. Frost, J. T. Oden, and L. C. Wellford, Jr., A Finite Element Analysis of Shock and Finite-Amplitude Waves in One-Dimensional Hyperelastic Bodies at Finite Strain, Int’l J. of Solids and Structures, (to appear).

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  5. J. T. Oden, J. E. Key, and R. B. Fost, A Note on the Analysis of Nonlinear Dynamics of Elastic Membranes by the Finite Element Method, Computers and Structures, Vol. 4, No. 2, 1974, pp. 445–452.

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  6. L. C. Wellford, Jr., and J. T. Oden, On Some Finite Element Methods for Certain Nonlinear Second Order Hyperbolic Equations, TICOM Report, 74–7, Austin, 1974.

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  7. L. C. Wellford, Jr., and J. T. Oden, A Theory of Discontinuous Finite-Element Galerkin Approximations of Shock Waves in Nonlinear Elastic Solids, TICOM Report, 74–6, Austin, 1974.

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  8. J. T. Oden, and L. C. Wellford, Jr., Finite Element Approximations of a Class of Nonlinear Two-Point Boundary Value Problems in Elasticity, TICOM Report, 74–5, Austin, 1974.

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  9. L. C. Wellford, Jr., and J. T. Oden, A Theory of Discontinuous Finite-Element Galerkin Approximations of Nonlinear Wave Phenomena, TICOM Report, 74–6, Austin, 1974.

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© 1975 Springer-Verlag

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Oden, J.T., Wellford, L.C. (1975). Continuous and discontinuous finite element approximations of shock waves in nonlinear elastic solids. In: Oden, J.T. (eds) Computational Mechanics. Lecture Notes in Mathematics, vol 461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074153

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  • DOI: https://doi.org/10.1007/BFb0074153

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07169-3

  • Online ISBN: 978-3-540-37503-6

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