Abstract-The use of wavelets has become increasingly popular in the development of numerical schemes for the solution of partial differential equations (PDEs), especially for problems with local high gradient. In this work, the Galerkin Method has been adapted for the direct solution of differential equations in a meshless formulation using Daubechies wavelets and Deslauriers-Dubuc interpolating functions (Interpolets). This approach takes advantage of wavelet properties like compact support, orthogonality and exact polynomial representation, which allow the use of a multiresolution analysis. Several examples based on typical differential equations for beams and thin plates were studied successfully.Index Terms-Wavelets, interpolets, wavelet-galerkin method, beam on elastic foundation, thin plates.
In this paper, a finite element model including both material heterogeneity and size effects is presented. The concrete is considered as a statistical combination of constituent phase with different properties (aggregate, mortar and interface material). The material point response is based on a combination of the random occurrence of the solid phases in the structural volume as well as on the differences of structural response due to the size effect. Such combination allows for higher or lower heterogeneity corresponding to smaller or larger structural size. Simulations of the material heterogeneity and associated size effect in a computationally efficient and simple manner show good qualitative agreement with available experimental results for the three-point bending and Brazilian split tests.
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