A BEM-based meshless solution to buckling and vibration problems of orthotropicplates

Tsiatas, George; Yiotis, Aristophanes J.

doi:10.1016/j.enganabound.2013.01.007

Cited by 15 publications

(4 citation statements)

References 14 publications

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“…For general boundary conditions, however, the analytical solution cannot be obtained due to the complexities introduced by the satisfaction of free edges and free corner boundary conditions. So, various approximate or numerical methods such as the Ritz method [1,7,8], the differential quadrature method (DQM) [9][10][11][12], the method of superposition [13], the extended Kantorovich approach [14,15], the spectral finite element method [16], the finite element method with basic displacement functions [17], the finite element method with isogeometric analysis [18], the mesh-free method [19], BEM-based meshless method [20], the moving least squares differential quadrature method [21], semi-analytic differential quadrature method [22], the projection equation approach [23], the finite difference method [24], the spectral element method [25], the discrete singular convolution method [26][27][28], the radial basis function-based DQM [29,30], the weak-form DQM [31], and the strong-form finite element method [32][33][34] have been developed to study the behavior of rectangular plates with general boundary conditions. Among the approximate analytical methods utilized for addressing the present problem, the Ritz method is one the most convenient methods to obtain the natural frequencies of rectangular plates [1,[35][36][37].…”

Section: Introductionmentioning

confidence: 99%

A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

Eftekhari

2016

Ain Shams Engineering Journal

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It is well known that the classical global approximation methods such as the conventional Ritz method and the conventional differential quadrature method (DQM) have some difficulty in determining the natural frequencies of rectangular plates involving free corners. The mixed Ritz-DQM formulation, which has been recently developed by the present author, was also shown to have such difficulty. This is because it is very difficult to implement the free corner boundary condition in these methods. To overcome this difficulty, this paper presents a mixed Ritz-DQM formulation in which the free corner boundary condition is implemented in a simple and easy manner. First, we present a new scheme for implementing multiple boundary conditions in the DQM discretized equations. By the help of this scheme, we then show that the free corner boundary condition can also be easily implemented in the final matrix equations of the Ritz-DQM approach. Finally, we validate the effectiveness of the proposed approach through numerical experiments. Numerical results show the advantages of the proposed method over some versions of the DQM in terms of accuracy and performance. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Section: Introductionmentioning

confidence: 99%

A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

Eftekhari

2016

Ain Shams Engineering Journal

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“…For the FEM, the large finite element mesh required to simulate wave propagation problems can be a significant limitation for its use. The BEM [6], [7] seems to be a very interesting alternative to the FEM, since it allows a very compact description of the propagation medium, requiring only discretization of the interfaces between different materials, and so it has indeed received great interest from the scientific community [8], [9]. However, the BEM also exhibits some limitations, since it produces fully filled equation systems, requires the previous knowledge of the fundamental solutions for the physical problem, and exhibits some additional mathematical complexity due to the need of calculating singular or quasi-singular integrals.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Buried Vibration Protection Devices Using the Method of Fundamental Solutions

Albino

Godinho

Dias-da-Costa

et al. 2019

Boundary Elements and Other Mesh Reduction Methods XLII

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Buried structures may be used to control elastic wave propagation in soils and help to reduce vibrations in sensitive structures. The analysis of these structures using numerical tools is of high importance and is usually a demanding computational task. In the present work, the authors explore the possibility of using a meshless method for such simulations, namely the method of fundamental solutions (MFS). In many applications, the MFS has proved to be a worthy and more efficient alternative to classic methods, such as the FEM or even the BEM. Here, the authors present a study on the application of the MFS to simulate the propagation of elastic waves in a soil with multiple buried inclusions. Application examples are also presented, in which the vibration reduction provided by different sets of buried inclusions is analysed and discussed.

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“…After the unknown displacement and traction on boundary are solved by the boundary integral equation, any physical values of interested interior points can be yielded successfully by the integral equations of interior points. The BEM has been successfully applied to solving multidiscipline problems, such as the potential problem (Zhou et al , 2008; Cheng et al , 2015), the elastic problem (Niu et al , 2005; Cheng et al , 2011) and the vibration problem (Zheng et al , 2016; Tsiatas and Yiotis, 2013). However, the FGM has to be divided into many subdomains when the conventional BEM is used to model it, which will increase the computational amount redundantly.…”

Section: Introductionmentioning

confidence: 99%

A state space boundary element method for elasticity of functionally graded materials

Chen

Han

Niu

et al. 2017

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Purpose The state space method (SSM) is good at analyzing the interfacial physical quantities in laminated materials, while it has difficulty in calculating the mechanical quantities of interior points, which can be easily evaluated by the boundary element method (BEM). However, the material has to be divided into many subdomains when the traditional BEM is applied to analyze the functionally graded material (FGM), so that the computational amount will be increased enormously. This study aims to couple these two methods to strengthen their advantages and overcome their disadvantages. Design/methodology/approach Herein, a state space BEM in which the SSM is coupled by the BEM is proposed to analyze the elasticity of FGMs, where one BEM domain is set and the others belong to SSM domains. The discretized elements occur only on the boundary of the BEM domain and at the interfaces between different SSM domains. In SSM domains, the horizontal interfaces of FGMs are discretized by linear elements and the variables along the vertical direction are yielded by the precise integration method. Findings The accuracy of the proposed method is verified by comparing the present results with the ones from the finite element method (FEM). It is found that the present method can provide accurate displacements and stresses in the FGMs by fewer freedom degrees in comparison with the FEM. In addition, the present method can provide continuous interfacial stresses at the interfaces between different material domains, while the interfacial stresses by the FEM are discontinuous. Originality/value The system equations of the state space BEM are built by combining the boundary integral equation with the state equations according to the continuity conditions at the interfaces. The mechanical parameters of any inner point can be evaluated by the boundary integral equation after the unknowns on the boundaries and interfaces are determined by the system equation.

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A BEM-based meshless solution to buckling and vibration problems of orthotropicplates

Cited by 15 publications

References 14 publications

A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

Numerical Analysis of Buried Vibration Protection Devices Using the Method of Fundamental Solutions

A state space boundary element method for elasticity of functionally graded materials

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