An effective high-order element for analysis of two-dimensional linear problem using SBFEM

A general solution procedure for the scaled boundary finite element method via shooting technique

In this paper, a coupled model based on finite element method (FEM), boundary element method (BEM) and scaled boundary FEM (SBFEM) (also referred to as the consistent infinitesimal finite element cell method) for dynamic response of 2D structures resting on layered soil media is presented. The SBFEM proposed by Wolf and Song (Finite-element Modelling of Unbounded Media. Wiley: England, 1996) and BEM are used for modelling the dynamic response of the unbounded media (far-field). The standard FEM is used for modelling the finite region (near-field) and the structure. In SBFEM, which is a semi-analytical technique, the radiation condition at infinity is satisfied exactly without requiring the fundamental solution. This method, also eliminates the need for the discretization of interfaces between different layers. In both SBFEM and BEM, the spatial dimension is decreased by one. The objective of the development of this coupled model is to combine advantages of above-mentioned three numerical models to solve various soil-structure interaction (SSI) problems efficiently and effectively. These three methods are coupled (FE-BE-SBFEM) via substructuring method, and a computer programme is developed for the harmonic analyses of SSI systems. The coupled model is established in such a way that, depending upon the problem and far-field properties, one can choose BEM and/or SBFEM in modelling related far-field region(s). Thus, BEM and/or SBFEM can be used efficiently in modelling the far-field. The proposed model is applied to investigate dynamic response of rigid and elastic structures resting on layered soil media. To assess the proposed SSI model, several problems existing in the literature are chosen and analysed. The results of the proposed model agree with the results presented in the literature for the chosen problems. The advantages of the model are demonstrated through these comparisons.

The dynamic response of the host structure to a high-frequency actuation is usually used for the detection of tiny damage in structures in the form of breathing crack. The simulation of the microcrack’s effect on the response is essential for several damage identification targets. The conventional finite element method suffers from very small mesh size requirements to address the high-frequency problems, resulting in very large mass and stiffness matrices. In this study, the scaled boundary finite element method was applied to model different schemes of structural health monitoring of a structure with breathing cracks based on high-frequency vibration. The scaled boundary finite element method discretizes only the boundary of the model and thus substantially reduces the size of structural matrices. The node-to-node contact strategy was introduced to the scaled boundary finite element method to capture the contact problem that occurs during the vibration of the breathing crack. As breathing crack vibration results in some nonlinear effects, the simulation of three phenomena was of interest: higher harmonic generation, frequency shift, and vibro-acoustic modulation. A shooting method was used for efficient time integration and description of the frequency response function in the nonlinear regime. According to the results, the scaled boundary finite element method is of great power, efficiency, and accuracy to treat the contact problems, especially in high-frequency regimes. Moreover, the nonlinear methods provide certain advantages over the linear techniques in the early detection of incipient damage.

The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique. combining the advantage of the finite element method (FEM) and the boundary element method (BEM) with unique properties of its own. In this paper, the SBFEM is used for computing wave passing a submerged breakwater, and the reflection coefficient and the transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater and a rigid submerged barrier breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is observed. Through compared with the results using the dual boundary element method (DBEM), it is found that the SBFEM could obtain the higher accuracy with fewer elements. Many submerged breakwaters with different demission are computed by the SBFEM, and the changing character of the reflection coefficient and the transmission coefficient are given in the current study.

A temporally piecewise adaptive multiscale scaled boundary finite element method to solve two-dimensional heterogeneous viscoelastic problems

ABSTRACTThis work explores the application of isogeometric scaled boundary method in the two-dimensional thermoelastic problems of irregular geometry. The proposed method inherits the advantages of both isogeometric analysis and scaled boundary finite element method and overcomes their respective disadvantages. In the proposed approach, the boundaries of the problem domain are discretized with nonuniform rational B-splines (NURBS) basis functions, while the temperature distributions inside the domain are represented by a sequence of power functions in terms of radial coordinate within the framework of scaled boundary finite element method. The resulting solution of the stress in radial direction can be computed analytically for the temperature changes. The construction of tensor product structure is circumvented for the two-dimensional problems as only the boundary information of the problem domain is required. Hence, the flexibility to represent the complex geometry can be significantly improved in the proposed method. Numerical examples are presented to validate the performance of the proposed method where it is seen that superior accuracy, efficiency, and convergence behavior can be achieved over the conventional scaled boundary finite element method.

A two-dimensional consistent approach for static and dynamic analyses of uniform beams

ABSTRACTNew semi‐analytical shell elements are developed using the scaled boundary finite element method. A shell element is treated as a three‐dimensional continuum whose midsurface, the generalized “boundary” of the continuum, is characterized with a quadrilateral spectral element. It is along the thickness direction ξ that the midsurface is scaled to represent the three‐dimensional geometry and that the analytical displacement solution is sought. Neumann expansion is used to approximate the inverse of the Jacobian as a quadratic matrix polynomial of ξ while the assumed natural strain method is applied to alleviate the shear and membrane locking. The virtual work principle considering body forces is utilized to derive the scaled boundary finite element equation, which is directly solved via the differential quadrature method. Numerical examples show that the shell elements with five displacement sampling points along ξ can efficiently analyze thin to very thick general shells.

The scaled boundary finite element method (SBFEM) has been used in many fields of engineering to solve the governing equations in bounded and unbounded 2D as well as 3D domains. In solid mechanics, the semi‐analytical solution strategy of the SBFE formulation (numerical in circumferential direction, analytical in radial direction) is based on the assumption of linear elastic material behavior and only small geometrical changes. However, a large group of materials (e.g. rubber) shows geometrical and physical nonlinearity at mechanical loading. In this contribution, the extension of the SBFEM to geometrical and physical nonlinearity is examined. A plane finite element is developed which uses the concept of shape functions constructed by the SBFEM in the framework of a nonlinear finite element analysis. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The scaled boundary finite element method based on the hybrid quadtree mesh for solving transient heat conduction problems

A high-order finite element technique with automatic treatment of stress singularities by semi-analytical enrichment

A scaled boundary isogeometric formulation for the elasto-plastic analysis of solids in boundary representation

A novel semi-analytical approach based on scaled boundary finite element method for fluid-structure coupling analysis of liquid sloshing in 3D containers

This study introduces a numerical framework for analysing hydrogen assisted cracking, employing the scaled boundary finite element method. This is the first instance where the scaled boundary finite element method is employed to model hydrogen embrittlement. The phase field model is utilized to simulate defects, complemented by adaptive meshing using polytree mesh. The ability of the scaled boundary finite element method to treat polygonal elements assists in mitigating the problem of hanging nodes that arises from polytree decomposition. The adaptive framework is developed to predict crack propagation using an initial unstructured quadrilateral mesh generated from any commercial software. The hydrogen atom concentration depends on the hydrostatic stress gradient, which is calculated by interpolating nodal hydrostatic stress with scaled boundary shape functions and taking the gradient. A staggered solution approach is adopted to concurrently tackle hydrogen transport, elasticity, and phase field equations. The methodology is validated using Mode-I edge notch specimens and analysing crack propagation from corrosion pits, with results demonstrating close agreement with existing data. Subsequently, the framework is extended to address more intricate scenarios, such as crack propagation in X-shaped plates and hydrogen transmission in tanks. As the last example, more advanced image based fracture analysis of weld structure is investigated. This example studies the possibility of analysing the hydrogen diffusion directly from TEM imagery. Moreover, we investigate how hydrogen concentration influences structural failure.

Magnetostatic simulations with consideration of exterior domains using the scaled boundary finite element method