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In this paper, a new semi-analytical method is developed with introducing a new global nonreflecting boundary condition at medium−structure interface, in which the coefficient matrices, as well as dynamic-stiffness matrix are diagonal. In this method, only the boundary of the problem's domain is discretized with higher-order sub-parametric elements, where special shape functions and higher-order Chebyshev mapping functions are employed. Implementing the weighted residual method and using Clenshaw–Curtis quadrature lead to diagonal Bessel's differential equations in the frequency domain. This method is then developed to calculate the dynamic-stiffness matrix throughout the unbounded medium. This method is a semi-analytical method which is based on substructure approach. Solving two first-order ordinary differential equations (i.e., interaction force–displacement relationship and governing differential equation in dynamic stiffness) allows the boundary condition of the medium−structure interface and radiation condition at infinity to be satisfied, respectively. These two differential equations are then diagonalized by implementing the proposed semi-analytical method. The interaction force–displacement relationship may be regarded as a nonreflecting boundary condition for the substructure of bounded domain. Afterwards, this method is extended to calculate the asymptotic expansion of dynamic-stiffness matrix for high frequency and the unit-impulse response coefficient of the unbounded media. Finally, six benchmark problems are solved to illustrate excellent agreements between the results of the present method and analytical solutions and/or other numerical methods available in the literature. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new semi-analytical method is presented for modeling of three-dimensional (3D) elastostatic problems. For this purpose, the domain boundary of the problem is discretized by specific subparametric elements, in which higher-order Chebyshev mapping functions as well as special shape functions are used. For the shape functions, the property of Kronecker Delta is satisfied for displacement function and its derivatives, simultaneously. Furthermore, the first derivatives of shape functions are assigned to zero at any given node. Employing the weighted residual method and implementing Clenshaw–Curtis quadrature, coefficient matrices of equations’ system are converted into diagonal ones, which results in a set of decoupled ordinary differential equations for solving the whole system. In other words, the governing differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. To evaluate the efficiency and accuracy of the proposed method, which is called Decoupled Scaled Boundary Finite Element Method (DSBFEM), four benchmark problems of 3D elastostatics are examined using a few numbers of DOFs. The numerical results of the DSBFEM present very good agreement with the results of available analytical solutions. [Copyright &y& Elsevier]

Abstract: In this paper, a novel semi-analytical method is proposed for modeling of two-dimensional (2D) elastodynamic problems. In this regard, the domain boundary of the problem is discretized by specific non-isoparametric elements that are proposed for the first time in this paper. In these elements, special shape functions as well as higher-order Chebyshev mapping functions are implemented. For the shape functions, Kronecker Delta property is satisfied for displacement function and its derivatives, simultaneously. Moreover, the first derivatives of shape functions are assigned to zero at any given node. Finally, using a weak form of weighted residual method and implementing Clenshaw–Curtis numerical integration, coefficient matrices of the system of equations are converted into diagonal ones, which leads to a set of decoupled partial differential equations for solving the whole system. This means that the governing partial differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. Also, to assess the accuracy and efficiency of the proposed method, four benchmark problems of 2D elastodynamics are solved using a few numbers of DOFs. The numerical results present excellent agreement with the analytical solutions and the results from other numerical methods. [Copyright &y& Elsevier]