Nonlinear Finite Element Analysis using an Object-Oriented Philosophy – Application to Beam Elements and to the Cosserat Continuum

Abstract.An Object-Oriented Programming (OOP) frame-work is presented for solving nonlinear structural mechanics problems by means of the Finite Element Method (FEM). Emphasis is placed on engineering applications (geometrically nonlinear beam model, and elastoplastic Cosserat continuum), and OOP is employed as an effective tool, which plays an important role in the FEM treatment of such applications. The implementation is based on computational abstractions of both mathematical and physical concepts associated to structural mechanics problems involving geometrical and material nonlinearities. The overall class organization for nonlinear mechanics modeling is discussed in detail. All the analyses rely on a generic control class where several classical and modern nonlinear solution schemes are available. Examples which explore, demonstrate and validate the main features of the overall computational system are presented and discussed.

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