Boundary element method analysis of assembled plate structures undergoing large deflection

2010 ◽  
Vol 45 (3) ◽  
pp. 179-195 ◽  
Author(s):  
C Di Pisa ◽  
M H Aliabadi ◽  
A Young
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Deflection ◽  
Equation System ◽  
Boundary Integral ◽  
Plate Structures ◽  
Linear Equation System ◽  
Non Linear ◽  
Interior Domain ◽  
Element Method

The boundary element method (BEM) for large deflection of shear deformable plates is reformulated to the case of multi-section assembled plate structures. Each plate section is modelled as a BEM region under membrane and bending loads, with force, moments, displacements, and rotations represented by generalized traction and displacement nodal variables on the boundary. Non-linear terms in the boundary integral formulation for each section that arises owing to large deflection are treated as effective body forces, and the associated domain integrals are transformed into boundary integrals using the dual reciprocity method. Derivatives of stresses and deflection on the boundary arise in the non-linear terms, and are evaluated by exploring their values at interior domain points using radial basis functions. Plate sections are joined along their edges using compatibility and equilibrium conditions involving the generalized traction and displacement nodal variables. The resulting non-linear equation system is solved numerically using an incremental load approach. An illustrative example of the method is presented for a transversely loaded plate reinforced with Z-stringers.

scholarly journals Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method

2007 ◽  
Vol 2007 ◽  
pp. 1-17 ◽  
Author(s):  
Luiz Carlos Facundo Sanches ◽  
Euclides Mesquita ◽  
Renato Pavanello ◽  
Leandro Palermo Jr.
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Mode Shapes ◽  
Plate Structures ◽  
Plane State ◽  
Reinforced Plate ◽  
Element Method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state (membrane) and for the out-of-plane state (bending). These uncoupled systems are joined to form a macro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

scholarly journals Development and Application of a Pre-Corrected Fast Fourier Transform Accelerated Multi-Layer Boundary Element Method for the Simulation of Shallow Water Acoustic Propagation

2020 ◽  
Vol 10 (7) ◽  
pp. 2393
Author(s):  
Chengxi Li ◽  
Jijian Lian
Keyword(s):  
Boundary Element Method ◽  
Shallow Water ◽  
Boundary Element ◽  
Sound Propagation ◽  
Water Environment ◽  
Equation System ◽  
Linear Equation System ◽  
Shallow Water Environment ◽  
Classical Boundary ◽  
Element Method

Because of the complexities associated with the domain geometry and environments, accurate prediction of acoustics propagation and scattering in realistic shallow water environments by direct numerical simulation is challenging. Based on the pre-corrected Fast Fourier Transform (PFFT) method, we accelerated the classical boundary element method (BEM) to predict the acoustic propagation in a multi-layer shallow water environment. The classical boundary element method formulate the acoustics propagation problem as a linear equation system in the form of [A]{x}={b}, where [A] is an N×N dense matrix composed of influence coefficients. Solving such linear equation system requires O(N2/N3) computational cost for iterative/direct methods. The developed method, PFFT-BEM, can effectively reduce the computational efforts for direct numerical simulations from O(N2~3) to O(Nlog N), where N is the total number of boundary unknowns. To numerically simulate the sound propagation in a shallow water environment, we applied the first-order non-reflecting boundary condition in the truncated numerical domain boundary to eliminate the errors due to reflected waves. Multi-layer coupled formulation was used to include the environment inhomogeneity in PFFT-BEM. Through multiple convergence tests on the number of layers and elements, we validated and quantified the accuracy of PFFT-BEM. To demonstrate the usefulness and capability of the developed PFFT-BEM, we simulated three-dimensional (3D) underwater sound propagation through 3D geometries to check the efficacy of the established classical method: the 3D Parabolic equation model. Finally, PFFT-BEM was employed to simulate sound propagation through a complex multi-layer shallow water environment with internal waves. The “3D+T” results obtained by PFFT-BEM compared well with the physical test, thereby proving the capability and correctness of this method.

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Large Scale ◽  
Boundary Integral ◽  
Practical Significance ◽  
Fast Multipole ◽  
Tree Structures ◽  
Wave Problems ◽  
Element Method

Some recent development of the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 2-D and 3-D domains are presented in this paper. First, the fast multipole BEM formulation for 2-D acoustic wave problems based on a dual boundary integral equation (BIE) formulation is presented. Second, some improvements on the adaptive fast multipole BEM for 3-D acoustic wave problems based on the earlier work are introduced. The improvements include adaptive tree structures, error estimates for determining the numbers of expansion terms, refined interaction lists, and others in the fast multipole BEM. Examples involving 2-D and 3-D radiation and scattering problems solved by the developed 2-D and 3-D fast multipole BEM codes, respectively, will be presented. The accuracy and efficiency of the fast multipole BEM results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale acoustic wave problems that are of practical significance.

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

scholarly journals Thermal Stress Analysis of 3D Anisotropic Materials Involving Domain Heat Source by the Boundary Element Method

2019 ◽  
Vol 35 (6) ◽  
pp. 839-850
Author(s):  
Y. C. Shiah ◽  
Nguyen Anh Tuan ◽  
M.R. Hematiyan
Keyword(s):  
Boundary Element Method ◽  
Heat Source ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Quadratic Function ◽  
Boundary Integral ◽  
Volume Integral ◽  
Direct Evaluation ◽  
Volume Heat ◽  
Element Method

ABSTRACTIn engineering applications, it is pretty often to have domain heat source involved inside. This article proposes an approach using the boundary element method to study thermal stresses in 3D anisotropic solids when internal domain heat source is involved. As has been well noticed, thermal effect will give rise to a volume integral, where its direct evaluation will need domain discretization. This shall definitely destroy the most distinctive notion of the boundary element method that only boundary discretization is required. The present work presents an analytical transformation of the volume integral in the boundary integral equation due to the presence of internal volume heat source. For simplicity, distribution of the heat source is modeled by a quadratic function. When needed, the formulations can be further extended to treat higher-ordered volume heat sources. Indeed, the present work has completely restored the boundary discretization feature of the boundary element method for treating 3D anisotropic thermoelasticity involving volume heat source.

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