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Trefftz and RBF-based formulations for concrete beams analysis using damage models

Tiago C. M., Castro Luis M.S.S., Leităo Victor M. A.

Computer Assisted Mechanics and Engineering Sciences

2003

Vol. 10, No. 4

641-660

In this work a hybrid-Trefftz formulation and a meshless approach based on the use of radial basis functions (RBF) are applied to the analysis of reinforced concrete beams. Resorting to the Mazars model, the concrete is represented by an elastic medium with progressive damage. In the hybrid-Trefftz formulation a stress field that satisfies a priori the equilibrium equations on the domain is used. The displacements on the static boundary are independently approximated, resulting in a governing system where the operators have to be integrated over the domain of the problem. In what concerns the meshless approach, radial basis functions are used to approximate the displacement fields but, as a collocation procedure is used, no integrations are required. A numerical example illustrates the results obtained with both techniques.

Thin plate bending analysis using an indirect Trefftz collocation method

Tiago C. M., Leitao V. M. A., Vasarhelyi A.

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 1

1--16

In this work, the application of an indirect Trefftz collocation method to the analysis of bending of thin plates (Kirchhoff's theory) is described. The deflection field approximation is obtained with the use of a set of functions satisfying a priori the homogeneous part of the differential equation of the problem. Each of the approximating functions is derived from a known thick plate solution. The boundary conditions are imposed by means of continuous (integral) and discrete (collocation) least squares methods. Numerical examples are presented and the accuracy of the proposed technique is assessed.