The principal aim of the current study is to examine a SCALED BOUNDARY Finite Element Method (SBFEM)-based model to analyze the interaction problem between the water waves and moored floating breakwaters with sharp edges. Regarding the increasing employment of rectangular cross-section floating breakwaters with vertical side plates to their down-wave and up-wave sides (π-shaped floating breakwaters), it can be stated that they are used as a practical basis to examine how the model works. By comparing the present solutions to those from existing literature, without changing the mesh density compared to previous simulations used in simple configurations, the accuracy and generality of the present model in the complex configurations are evaluated. It is demonstrated that as the proposed model is a semi-analytical method, unlike conventional numerical methods, there is no need to refine the mesh around sharp corners, which can considerably save the computational time, effort, and cost in large solution domains.

In this study, a new computational scheme called the SCALED BOUNDARY finite-element method (SBFEM) is employed to analyze confined seepage flow. This technique combines the advantages of both finite-element and BOUNDARY element methods, i. e., only the BOUNDARY is discretized, no fundamental solution is required, unbounded domains and singularity points are modeled rigorously, and finally anisotropic materials and non-homogenous materials satisfying similarity can be modeled without additional computational efforts. In this paper, after presenting formulation of the method for solving confined seepage problems, selected problems using this method are analyzed and the results are compared with the results of other numerical methods. High accuracy and efficiency of this method is demonstrated.

It is possible to resolve numerical issues by utilizing a method known as the conventional SCALED BOUNDARY finite element method (also known as SBFEM), which is a dimension reduction technique. This method can be utilized in conjunction with mesh-free technologies to enhance the numerical characteristics of the conventional SBFEM. Within the scope of this investigation, a novel interpretation of the SBM is presented that makes use of the advantages offered by the meshless local Petrov Galerkin method. Using the moving Kriging interpolation (MKI) method, one can create shape functions that conform to the requirements of the Kronecker delta function property. The interpolating SCALED BOUNDARY local Petrov Galerkin method that was proposed then can implement essential BOUNDARY conditions (ISBLPGM) directly. This new method offers a number of benefits in comparison to SCALED BOUNDARY approaches that have been presented in the past. It is optional to have a mesh that has been predefined, and the BOUNDARY conditions can be determined with very little additional effort. It has been demonstrated that the numerical approach that is being presented yields results that are in very good agreement with analytical and other numerical approaches. Solving the benchmark numerical problems allows for an evaluation of the effectiveness of the proposed method as well as its precision

Wave propagation in unbounded layered media with a new formulation of Axisymmetric SCALED BOUNDARY Finite Element Method (AXI-SBFEM) is derived. Dividing the general three-dimensional unbounded domain into a number of independent two-dimensional ones, the problem could be solved by a significant reduction in required storage and computational time. The equations of the corresponding Axisymmetric SCALED BOUNDARY Finite Element (AXI-SBFE) are derived in detail. For an arbitrary excitation frequency, the dynamic stiffness could be solved by a numerical integration method. The dynamic response of layered unbounded media has been verified with the literature. Numerical examples indicate the applicability and high accuracy of the new method.

In this paper, an effective SCALED BOUNDARY spectral element method is used to analyze seismic soil-structure interaction (SSSI) problems. Coefficient matrices are lumped by using Gauss-Lobatto-Legendre (GLL) quadrature and Lagrange interpolation functions. Required storage space of the computers can be reduced by using lumped coefficient matrices. In addition, a recursive algorithm is adapted to reduce computational effort of the seismic soilstructure interaction analysis. Adapted recursive algorithm can reduce computational effort of the original SCALED BOUNDARY method (SBM) about 90%. Efficiency of the proposed method is displayed by solving some numerical examples. It is shown that accuracy of the semi local SBM depends on the selected cut off time step.

A novel element with arbitrary domain shape by using decoupled SCALED BOUNDARY finite element (DSBFEM) is proposed for eigenvalue analysis of 2D vibrating rods with different BOUNDARY conditions. Within the proposed element scheme, the mode shapes of vibrating rods with variable BOUNDARY conditions are modelled and results are plotted. All possible conditions for the rods ends are incorporated in analysis. The considered element stiffness and mass matrix are developed and extracrted. This element is able to model any curved or sharp edges without any aproximation and also the element is able to model any arbitrary domain shape as a single element without any meshing. The coefficient matrices for the element such as mass and stiffness matrices are diagonal symmetric and all equations are decoupled by using Gauss-Lobatto-Legendre (G. L. L) quadrature. The element is used in order to calculate modal parameters by Finite element method for some benchmark examples and comparing the answers with Helmholtz equation solution. The most important achievment of this element is solving matrix equations instead of differential equations where cause faster calculations speed. The boundaries for this element are solved with matrix calculation and the whole interior domain with solving governing equations numerically wich leads us to an exact answer in whole domain. The introduced element is applied to calculate some benchmark example which have exact solution. The results shows accuracy and high speed of calculation for this method in comparison with other common methods.

Ground surface with irregular topography is one of the reasons of complex seismic responses, which are mainly due to the seismic wave scattering at ground surface. More investigation is needed for understanding the influence of wave scattering in specific places of ground surface. In this paper, the surface soil assumed homogeneous, isotropic, and elastic. At first, SH wave propagation equations in a two dimensional field by the SCALED BOUNDARY finite element method have been presented. This method has been developed by combining advantages of the finite element and BOUNDARY element methods. In this method, only the BOUNDARY is discretized and no fundamental solution or Green's function is required. Then a semi-circular hill has been analyzed by using this method. The results of this analysis compared with other analytical and numerical methods and good agreement is achieved.

Structures are subjected to different loadings during their lifetime. Most of these loads are time dependent and change over the time. Therefore, it is important to evaluate structures under dynamic loads. On the other hand, dynamic response of structures is affected by several factors that results in many complexities to structural analysis. Thus, numerical methods are used for seismic analysis of structures. In this article, a new semi analytical method with high efficiency is developed for soil-structure interaction (SSI) analysis, which is called decoupled SCALED BOUNDARY finite element method (DSBFEM). This method has analytical solution in radial direction and uses a specific shape functions as the interpolation function in the circumferential direction. In addition, the boundaries of the problem are discretized by specific new nonisoparametric elements. In these elements, new 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, simultaneously. Moreover, the first derivatives of shape functions are assigned to zero at any given control point. In fact, to model the geometry of the problems, we consider a local coordinate origin (LCO) for transportation of the geometric characteristics of global coordinate and local coordinate. Consequently, using a 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. Due to the soil flexibility effect on structural responses, in this paper, SSI problem has been investigated considering different values of modulus of elasticity for soil domain. To achieve this, two different LCOs have been used to discretize the soil domain and the structure domain. Thus, a three-step algorithm is proposed, which consists of: (1) considering an initial stress on the interaction BOUNDARY, (2) analysis of soil domain, and (3) analysis of structure domain. Therefore, after the initial assumption of stress on the interaction BOUNDARY, the soil domain will be completely analyzed by two-stage traction redistribution and the results on interaction BOUNDARY will be used as BOUNDARY conditions of structure domain. It should be noted that in the proposed algorithm, only one-stage traction redistribution will be used to analyze the structure domain. Finally, validity and accuracy of DSBFEM are fully demonstrated through some benchmark examples with different values of modulus of elasticity for the soil domain, and the results are compared with Finite Element Method (FEM). The results indicate that the proposed method has high accuracy and flexibility to consider the SSI effect, determine the resonant frequency and the maximum displacement amplitude of the structure. In addition, the number of elements used in the DSBFEM is much less than the FEM, which will lead to a reduction in computational costs.

Continuity and discontinuity of two-dimensional domains are thoroughly investigated for accuracy and convergence rate using two prominent discretization methods, namely smoothed and SCALED BOUNDARY finite element. Because of their capability and versatility when compared to primitive elements, N-sided polygonal elements discretized from modified DistMesh and PolyMesher schemes are used. In terms of accuracy and convergence rate, NSFEM and SBFEM are found to be superior to CSFEM and ESFEM regardless of meshing alternative. The best accuracy occurs at NSFEM and SBFEM, and the obtained convergence rates are optimal. Particularly, in the smoothing domain, it is believed that DistMesh has more promising potential than PolyMesher does; yet, in the discontinuity domain, PolyMesher has been discovered to be more powerful while maintaining its efficiency.