共查询到19条相似文献,搜索用时 181 毫秒
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基于传递矩阵法、齐次扩容精细积分法和复数矢径虚拟边界谱方法 ,提出了一种求解水下非圆弹性环声散射问题的半解析方法。该方法具有以下几个优点 :(1)采用复数矢径虚拟边界谱方法 ,不仅能保证在全波数域内Helmholtz外问题解的唯一性 ,而且由于虚拟源强密度函数采用 Fourier级数展开 ,克服了用单元离散解法不能用于较高频率范围的缺点 ;(2 )采用齐次扩容精细积分法求解非圆弹性环的状态微分方程 ,其计算结果具有很高的精度 ;(3)耦合方程不需要交错迭代求解 ,提高了计算效率。文中给出了两个典型非圆弹性环在平面声波激励下的声散射算例 ,计算结果表明本文方法是一种求解二维非圆弹性环声散射问题非常有效的半解析法。 相似文献
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本文基于有限水深带形域势流问题的基本解和二维线弹性力学问题的Kelvin解,建立了坝库系统在谐激励下稳态响应的双边界积分方程.推导过程中,利用了Nardini和Brebbia方法将分布惯性力项的体积分化为相应的边界积分.然后通过边界元离散技术,针对两个不同型式的坝体计算了作用在界面上的水动压力分布,其中一个算例的结果和已有的有限元解作了比较. 相似文献
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一种无奇异积分的边界单元法 总被引:5,自引:0,他引:5
处理基本解的奇异性是边界单元法的难题之一。本文避开奇异基本解,用非奇异基本解建立边界积分方程。非奇异基本解取自齐次微分方程的一般解和完备系,使求解边界积分方程容易。文中对边界未知量采用样条插值函数,计算精度良好。 相似文献
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将准Green函数方法应用于求解夹支任意形状底扁球壳的自由振动问题。即利用问题的基本解和边界方程构造一个准Green函数,这个函数满足了问题的齐次边界条件。采用Green公式将夹支任意形状底扁球壳自由振动问题的振型控制微分方程化为第二类Fredholm积分方程。通过边界方程的适当选择,克服了积分方程核的奇异性。最后通过离散化方程求得数值结果。数值算例表明:该方法具有较高的精度、计算量小、收敛速度快,是一种新型有效的数学方法。 相似文献
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本本文给出了三维无限大域内点热源作用下的位移、应力场基本解。采用基于虚拟热源法的间接边界元法和直接边界元法的混合边界元法求解三维有限域热弹性力学问题,有效地避免了热弹性力学问题中域内积分的处理。数值计算表明混合边界元法求热弹性力学问题具有简单方便、精度较高的优点。 相似文献
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《Engineering Analysis with Boundary Elements》1999,23(3):247-256
A boundary element method (BEM) approach for the solution of the elastic problem with geometrical non-linearities is proposed. The geometrical non-linearities that are considered are both finite strains and large displacements. Material non-linearities are not considered in this paper, so the constitutive law employed is Hooke's elastic one and the fundamental solution introduced in the integral equations is the usual one for isotropic linear elasticity. In order to deal with the intricate non-linear equations that govern the problem, an incremental–iterative method is proposed. The equations are linearized and a Total Lagrangian Formulation is adopted. The integral equations of the BEM are developed in an incremental form. The iterative process is necessary in order to achieve a good approximation to the governing equations. The problem of a slab under homogeneous deformation is solved and the results obtained agree with the analytical solution. The problem of a hollow cylinder under internal pressure is also solved and its solution compared with that obtained by a standardized finite element method code. 相似文献
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针对非线性振动激励下结构声辐射问题,由变分原理导出Duffing振子激励下平板声振耦合动力学方程,由模态展开法及增量谐波平衡法导出轻流体中耦合动力学方程的近似解析解,给出多频激励下平板表面平均振速及辐射声功率表达式,研究激励力频率、非线性项对系统振动及声辐射特性影响。结果表明,Duffing振子激励下平板的声振耦合问题为含离散与连续系统的复杂动力学问题;耦合运动下Duffing振子出现二次跳跃现象与新的共振特性;平板声振特性主要由三次谐波决定。研究结果可为隔振结构的声振设计提供理论依据。 相似文献
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The boundary knot method is a promising meshfree, integration-free, boundary-type technique for the solution of partial differential equations. It looks for an approximation of the solution in the linear span of a set of specialized radial basis functions that satisfy the governing equation of the problem. The boundary conditions are taken into account through the collocation technique. The specialized radial basis function for harmonic elastic and viscoelastic problems is derived, and a boundary knot method for the solution of these problems is proposed. The completeness issue regarding the proposed set of radial basis functions is discussed, and a formal proof of incompleteness for the circular ring problem is presented. In order to address the numerical performance of the proposed method, some numerical examples considering simple and complex domains are solved. 相似文献
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This study details the development of boundary integral equations suitable for treating problems involving the scatter of a plane harmonic wave by an inclusion embedded in an infinite poroelastic medium. The pore pressure-solid displacement form of the harmonic equations of motion are developed from the form of the equations originally presented by Biot. Fundamental solutions and a generalized reciprocal work relation are developed, and these are used to formulate a solution representation in terms of an integral over the inclusion surface. The corresponding boundary integral equations are developed in a form that is integrable in the usual sense, eliminating the need to evaluate Cauchy principal value integrals. These boundary integral equations are discretized and implemented into a boundary element computer program. The so-called forbidden frequency problem which causes computational difficulties in boundary integral treatments of wave scatter in elastic and acoustic media is shown to be absent in the poroelastic case. Numerical results obtained from the boundary element program are compared with analytical results for some test problems, and the program appears to produce accurate results at moderate frequencies. 相似文献
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Summary An asymptotic approach to dynamic interaction between a few distant dies and an elastic half-space is proposed. The transient motion of the dies under low-frequency vertical load is under consideration. The explicit expression for the fundamental singular solution of Lamb's problem is used to derive the boundary integral equation of contact. Then this equation is asymptotically simplified and solved numerically in combination with equations of motion of the dies.Equations obtained in the asymptotic limit describe both the die-medium dynamic interaction and the interaction between dies through the elastic medium. These equations take into account the energy dissipation phenomenon associated with energy transfer deep into the medium by outgoing elastic waves, of so called geometrical damping.Equations proposed are asymptotically correct within the corresponding range of parameters, as such improving the state-of-the-art. 相似文献
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G. D. Manolis D. E. Beskos 《International journal for numerical methods in engineering》1981,17(4):573-599
The dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined. The material may be linear elastic or viscoelastic, while the dynamic load consists of plane compressional waves of harmonic or general transient nature. The method consists of applying the Laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method. The stress field can then be obtaind by a numerical inversion of the trasformed solution. The correspondence principle is invoked for the case of viscoelastic material behavious. The method is simplified for the case of harmonic waves where no numerical inversion is involved. 相似文献
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Menshykov OV Guz IA Menshykov VA 《Philosophical transactions. Series A, Mathematical, physical, and engineering sciences》2008,366(1871):1835-1839
The paper concerns the validation of a method for solving elastodynamics problems for cracked solids. The proposed method is based on the application of boundary integral equations. The problem of an interface penny-shaped crack between two dissimilar elastic half-spaces under harmonic loading is considered as an example. 相似文献
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In this paper, the contact problem between a rigid indenter and a viscoelastic half space containing either isotropic or anisotropic elastic inhomogeneities is solved. The model presented here is 3D and based on semi-analytical methods. To take into account the viscoelastic properties of the matrix, contact and subsurface problem equations are discretized in the spatial and temporal dimensions. A conjugate gradient method and the fast Fourier transform are used to solve the normal problem, contact pressure, subsurface problem and real contact area simultaneously. The Eshelby’s formalism is applied at each step of the temporal discretization to account for the effect of the inhomogeneity on pressure distribution and subsurface stresses. This method can be seen as an enrichment technique where the enrichment fields from heterogeneous solutions are superimposed to the homogeneous viscoelastic problem solution. Note that both problems are fully coupled. The model is validated by comparison with a Finite Element Model. A parametric analysis of the effect of elastic properties and geometrical features of the inhomogeneity is proposed. The model allows to obtain the contact pressure distribution disturbed by the presence of inhomogeneities as well as subsurface and matrix/inhomogeneity interface stresses at every step of the temporal discretization. 相似文献
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Vibration isolation using open or filled trenches 总被引:12,自引:0,他引:12
The problem of structural isolation from ground transmitted vibrations by open or infilled trenches under conditions of plane strain is numerically studied. The soil medium is assumed to be linear elastic or viscoelastic, homogeneous and isotropic. Horizontally propagating Rayleigh waves or waves generated by the motion of a rigid foundation or by surface blasting are considered in this work. The formulation and solution of the problem is accomplished by the boundary element method in the frequency domain for harmonic disturbances or in conjunction with Laplace transform for transient disturbances. The proposed method, which requires a discretisation of only the trench perimeter, the soil-foundation interface and some portion of the free soil surface on either side of the trench appears to be better than either finite element or finite difference techniques. Some parametric studies are also conducted to assess the importance of the various geometrical, material and dynamic input parameters and provide useful guidelines to the design engineer. 相似文献