engleski

Collocation method with Fup basis functions in modeling solid mechanics problems

This paper presents the results of research in development and application of Fup basis functions in a collocation method that can effectively solve various solid mechanics problems. Fup basis functions belong to the class of atomic basis functions of algebraic type introduced in [1] and can be regarded as infinitely derivable splines. Their important properties [2], such as localization through the compact support, good approximation properties linked with exact presentation of algebraic polynomials, partition of unity and desired level of continuity, enable an efficient numerical modeling either by implementation in the weak formulation (Galerkin and finite volume) or in the strong formulation (collocation). Numerical solutions in this paper were obtained using a collocation method that ensures that predefined mesh and numerical integration are avoided. The advantages of the proposed method have been highlighted in solving non-linear problems in structural mechanics (elasto-plastic analyses of beam bending) where numerical procedure is stable until plastic failure occurs. Application in the analysis of thin plate bending proved to be very efficient in comparison to conventional finite elements due to enhanced continuity, higher order and superior approximation properties of Fup basis functions. Particular difficulty presents description of irregular geometry because Fup basis functions in higher dimensions are obtained by tensor product. Problem can be solved by combining the collocation method with Fup basis functions and the solution structure method which enables exact treatment of all prescribed boundary conditions and to describe the geometry of the domain exactly in analytical form. This combined method is illustrated in solving the general problem of the torsion of a prismatic bar.

atomic functions ; collocation ; plastic failure ; solution structure ; boundary conditions

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