engleski

A New Finite Element for Higher Order Continuum Theory

Heterogeneous microstructure is present in all engineering materials, and an accurate description of microstructural behavior is necessary in order to correctly predict behavior of macrostructure. Classical continuum mechanics uses local approach and is unable to describe the effect of the microstructural size. Using higher – order continuum theory, which includes microstructural parameter in its formulation, enables to properly model microstructure of a given material. This contribution deals with a new finite element which can be used for modeling heterogeneous materials using higher – order theories. The proposed element is two – dimensional, four node triangle, with displacements and first derivations of displacements as degrees of freedom in corner nodes, and displacements as degrees of freedom in node positioned at triangle centroid in order to satisfy full interpolation polynomial of third degree. The finite element is developed using displacement based method [1] in Cartesian coordinate system and yields linear deformations and constant second-order deformations, and satisfies semi C1 continuity. Such element is feasible for implementation of both classical continuum theory as well as higher – order theories. In this contribution, Aifantis theory of gradient elasticity [2], which is a simplification of more general gradient theory developed by Mindlin [3], is implemented in the finite element formulation. The research proposed continues work performed by Lesičar et al. [4], where the C1 finite element in triangular coordinate system has been developed. The benchmark and patch test results, as well as the comparison between previously developed and new element, are reported in numerical examples.

finite element, C1 continuity, Aifantis theory of gradient elasticity

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