In the nonlinear vibrations of structural systems, the actual stress strain variation of their material is closely approximated by continuous functions of stress versus the strain. The function of stress can be adjusted to describe the stress strain diagrams for various materials, like: steel, aluminium, concrete, etc., by varying the parameters related to the material properties. The continuous variation of the stresses from linear to nonlinear elastic to plastic states, during loading and unloading is included in the formulation. The geometrical nonlinearity is introduced in the derivations. The dynamic analysis is based on linear acceleration approaches and is performed by lumped mass or consistent mass method by using either an iterative approach or an incremental approach or by using an iterative process within each iteration. The software STDYNL, is modified to include the new formulations. Illustrative examples are provided in order to compare the results obtained with those solved previously.

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