Abstract
A simple method to analysis any arbitrary domain shapes with a single element which based on Decoupled Scaled Boundary Finite Element Method is presented in this paper. The introduced element is based on boundary finite element method which helps to modelling curve and sharp boundaries with acceptable accuracy. Shape functions and mapping functions are similar to Decoupled Scaled Boundary Finite Element Method but locating center origin (LCO) is relocated in this method from corners with direct view to whole domain into shape center and formulation and behavior of the method is developed for the element. The most important advantageous of this technique is ability of solving displacement in domain by solving differential equations which causes more accurate answers in domain. We also perform well-established numerical tests and show the performance of the new element. Results shown us the accuracy and reliable answers for the introduced element. Also some benchmark examples are solved by this method and answers are compared with correct answers and plotted. High accuracy of answers with low cost of calculations and ability of the method to analysis the curve and sharp boundaries are the most important advantageous of this new element.
Highlights
It is well known that 2D problems can be applied in engineering as well and the results can be reliable for engineering decision
Various types of numerical methods such as Finite Element Method (FEM), Boundary Element Method (BEM), Scaled Boundary Methods (SBFEM), and mesh-less methods are commonly used in order to solve elasto-static and elasto-dynamic problems in two-dimensional problems [1,2,3] and simulating cracks and fractures in domains [4,5]
First to interpolate the boundaries and second for calculating in domain. This element is made of DSBFEM and general formulation of that technique is acceptable in this method, so boundaries strains can be calculated by the methods of that technique and domain strains can be calculated by solving differential equations
Summary
It is well known that 2D problems can be applied in engineering as well and the results can be reliable for engineering decision. Various types of numerical methods such as Finite Element Method (FEM), Boundary Element Method (BEM), Scaled Boundary Methods (SBFEM), and mesh-less methods are commonly used in order to solve elasto-static and elasto-dynamic problems in two-dimensional problems [1,2,3] and simulating cracks and fractures in domains [4,5] All these methods have their own advantageous and disadvantageous. In this paper we use Decoupled Scaled Boundary Finite Element Method in order to solve whole domain by finite element rules In this way first we divide the boundaries into some nodes (Gaussian nodes) and we locate the Locating Coordinate Origin (LCO) at the center of area of the domain shape. The results shown high accuracy and reliable answers for the suggested method
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