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1.
Fariba Takhtabnoos 《Inverse Problems in Science & Engineering》2018,26(11):1676-1694
In this paper, we consider coefficient inverse problems, which are associated with the identification of unknown time dependent control parameter and unknown solution of two-dimensional parabolic inverse problem with overspecialization at a point in the spatial domain. After suitable finite difference approximation of time variable, an MLPG method is used for spatial discretization. To improve the efficiency of the MLPG method, a greedy algorithm is used. In fact, using the greedy algorithm, we avoid using more points from the data site than absolutely necessary and therefore, the method becomes more efficient. Comparison of the different kind of point selection and the effect of noisy data are performed for four test problems while our last test problem considers a problem with unknown solution. The results reveal that the method is efficient. 相似文献
2.
A. AbdollahifarM.R. Nami A.R. Shafiei 《Engineering Analysis with Boundary Elements》2012,36(3):451-457
This paper introduces a novel meshless local Petrov-Galerkin (MLPG) method by presenting a new test function as a schema to solve the elasto-static problems. It is seen that the four ordinary MLPG methods can also be approached using the present test function. Both the moving least square (MLS) and the direct method have been applied to the method to estimate the shape function and to impose the essential boundary conditions. The results of three studied elasto-static cases; “two dimensional cantilever beam”, “first mode fracture of a center-cracked strip” and “edge-cracked functionally graded strip” show that by using less number of nodes, the present work gives sufficiently more accurate results. Meanwhile the method can also unify various kinds of MPLGs and one may conclude that the model is a good replacement for other common approaches. 相似文献
3.
无网格局部Petrov-Galerkin(MLPG)方法是一种新型的数值方法,它不需要任何形式的网格划分,所有的积分都在规则形状的子域及其边界上进行,并用罚因子法施加本质边界条件。MLPG方法处在发展中,关于其求解效率、精度以及可应用的领域等方面的研究非常有限,有待大力改进和完善。本文采用MLPG分析轴对称问题,将三维空间问题简化到平面内进行求解,通过加权余量法导出了轴对称问题无网格局部Petrov-Galerkin(MLPG)方法的计算公式,编制了相应的计算程序,对轴对称薄板分别进行了静力学和动力学分析,得到令人满意的数值结果。通过与其它方法的结果相比较,讨论了本文方法的有效性。 相似文献
4.
为了提高无网格方法计算振动问题时的计算效率和计算精度,开发了无网格时域自适应算法。该方法在时域内采用时域自适应算法,将每个变量在每个时间步内离散成关于时间的展开形式,通过控制展开阶数保证自适应算法的精度,可以更准确的描述变量随时间的变化;同时将时空耦合的初值问题转化为一系列的空间边值问题,并采用无网格方法递推求解。该方法可以提高计算效率并弥补时间步长较多或较大时造成的精度损失,并通过数值算例验证了其准确性。 相似文献
5.
SSPH basis functions for meshless methods, and comparison of solutions with strong and weak formulations 总被引:1,自引:0,他引:1
We propose a new and simple technique called the Symmetric Smoothed Particle Hydrodynamics (SSPH) method to construct basis
functions for meshless methods that use only locations of particles. These basis functions are found to be similar to those
in the Finite Element Method (FEM) except that the basis for the derivatives of a function need not be obtained by differentiating
those for the function. Of course, the basis for the derivatives of a function can be obtained by differentiating the basis
for the function as in the FEM and meshless methods. These basis functions are used to numerically solve two plane stress/strain
elasto-static problems by using either the collocation method or a weak formulation of the problem defined over a subregion
of the region occupied by the body; the latter is usually called the Meshless Local Petrov–Galerkin (MLPG) method. For the
two boundary-value problems studied, it is found that the weak formulation in which the basis for the first order derivatives
of the trial solution are derived directly in the SSPH method (i.e., not obtained by differentiating the basis function for
the trial solution) gives the least value of the L2-error norm in the displacements while the collocation method employing the strong formulation of the boundary-value problem
has the largest value of the L2-error norm. The numerical solution using the weak formulation requires more CPU time than the solution with the strong formulation
of the problem. We have also computed the L2-error norm of displacements by varying the number of particles, the number of Gauss points used to numerically evaluate domain
integrals appearing in the weak formulation of the problem, the radius of the compact support of the kernel function used
to generate the SSPH basis, the order of complete monomials employed for constructing the SSPH basis, and boundary conditions
used at a point on a corner of the rectangular problem domain. It is recommended that for solving two-dimensional elasto-static
problems, the MLPG formulation in which derivatives of the trial solution are found without differentiating the SSPH basis
function be adopted. 相似文献
6.
Free and Forced Vibrations of a Segmented Bar by a Meshless Local Petrov–Galerkin (MLPG) Formulation
We use the meshless local Bubnov–Galerkin (MLPG6) formulation to analyze free and forced vibrations of a segmented bar. Three
different techniques are employed to satisfy the continuity of the axial stress at the interface between two materials: Lagrange
multipliers, jump functions, and modified moving least square basis functions with discontinuous derivatives. The essential
boundary conditions are satisfied in all cases by the method of Lagrange multipliers. The related mixed semidiscrete formulations
are shown to be stable, and optimal in the sense that the ellipticity and the inf-sup (Babuška-Brezzi) conditions are satisfied.
Numerical results obtained for a bimaterial bar are compared with those from the analytical, and the finite element methods.
The monotonic convergence of first two natural frequencies, first three mode shapes, and a static solution in the L
2, and H
1 norms is shown. The relative error in the numerical solution for a transient problem is also very small. 相似文献
7.
8.
Piezoelectric materials have wide range engineering applications in smart structures and devices. They have usually anisotropic properties. Except this complication electric and mechanical fields are coupled each other and the governing equations are much more complex than that in the classical elasticity. Thus, efficient computational methods to solve the boundary or the initial-boundary value problems for piezoelectric solids are required. In this paper, the Meshless local Petrov-Galerkin (MLPG) method with a Heaviside step function as the test functions is applied to solve two-dimensional (2-D) piezoelectric problems. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the time-dependence in the governing partial differential equations the Laplace-transform technique is applied to the governing equations, which are satisfied in the Laplace-transformed domain in a weak-form on small subdomains. Nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity. The spatial variation of the displacements and the electric potential are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations, one obtains a system of linear algebraic equations for unknown nodal values. The boundary conditions on the global boundary are satisfied by the collocation of the MLS-approximation expressions for the displacements and the electric potential at the boundary nodal points. The Stehfest's inversion method is applied to obtain the final time-dependent solutions. 相似文献
9.
The Rajendran-Grove (RG) ceramic damage model is a three-dimensional internal variable based constitutive model for ceramic materials, with the considerations of micro-crack extension and void collapse. In the present paper, the RG ceramic model is implemented into the newly developed computational framework based on the Meshless Local Petrov-Galerkin (MLPG) method, for solving high-speed impact and penetration problems. The ability of the RG model to describe the internal damage evolution and the effective material response is investigated. Several numerical examples are presented, including the rod-on-rod impact, plate-on-plate impact, and ballistic penetration. The computational results are compared with available experiments, as well as those obtained by the popular finite element code (Dyna3D). 相似文献
10.
Jin?Yeon?ChoEmail author Young?Burm?Jee 《Journal of Mechanical Science and Technology》2003,17(7):986-998
In this paper, an adaptive numerical integration scheme, which does not need non-overlapping and contiguous integration meshes,
is proposed for the MLPG (Meshless Local Petrov-Galerkin) method. In the proposed algorithm, the integration points are located
between the neighboring nodes to properly consider the irregular nodal distribution, and the nodal points are also included
as integration points. For numerical integration without well-defined meshes, the Shepard shape function is adopted to approximate
the integrand in the local symmetric weak form, by the values of the integrand at the integration points. This procedure makes
it possible to integrate the local symmetric weak form without any integration meshes (non-overlapping and contiguous integration
domains). The convergence tests are performed, to investigate the present scheme and several numerical examples are analyzed
by using the proposed scheme. 相似文献