# Finite Element Formulations of Solid Continua

# Finite Element Formulations of Solid Continua

This chapter discusses the nonlinear continuum finite element formulation of elastic solids and presents updated and total Lagrangian finite element formulations using the principle of virtual displacements. Finite element models of plane elastic solids and shells are included as special cases. Several examples of application of the continuum plane elasticity and shell elements are presented. Lastly, the refined nonlinear shell element based on assumed displacement field that accounts for thickness stretch, the use of three-dimensional constitutive relations, and high-order spectral/*hp* approximations is presented. The shell element is based on a modified first-order shell theory kinematics that involves a 7-parameter expansion of the displacement field.

*Keywords:*
mathematical models, finite element method, elastic solids, virtual displacements, nonlinear shell element

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