共查询到10条相似文献,搜索用时 218 毫秒
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本文利用摄动的思想,以摄动有理曲线(曲面)的系数的无穷模作为优化目标,给出了用多项式曲线(曲面)逼近有理曲线(曲面)的一种新方法.同以前的各种方法相比,该方法不仅收敛而且具有更快的收敛速度,并且可以与细分技术相结合,得到有理曲线与曲面的整体光滑、分片多项式的逼近. 相似文献
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An efficient method of solving 3D elasticity problems for thick and thin laminated composite plates is presented. It is based
on a new concept of reference surfaces inside the plate. According to this concept, into each nth layer, In arbitrary reference
surfaces parallel to the midsurface are introduced, and the displacement vectors of these surfaces are chosen as unknown functions.
Such a choice allows one to represent the governing equations of the high-order theory of plates proposed in a very compact
form and to derive strain–displacement relationships correctly describing all rigid-body motions of laminated plates. 相似文献
4.
We present an algorithm for uniformly distributed circular porous pattern generation on surface for three-dimensional (3D) printing using a phase-field
model. The algorithm is based on the narrow band domain method for the nonlocal
Cahn–Hilliard (CH) equation on surfaces. Surfaces are embedded in 3D grid and the
narrow band domain is defined as the neighborhood of surface. It allows one can
perform numerical computation using the standard discrete Laplacian in 3D instead
of the discrete surface Laplacian. For complex surfaces, we reconstruct them from
point cloud data and represent them as the zero-level set of their discrete signed
distance functions. Using the proposed algorithm, we can generate uniformly distributed circular porous patterns on surfaces in 3D and print the resulting 3D models.
Furthermore, we provide the test of accuracy and energy stability of the proposed
method. 相似文献
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《Finite Elements in Analysis and Design》2002,38(4):337-352
In this paper, we develop and implement a new method for the accurate representation of contact surfaces. This approach overcomes the difficulties arising from the use of traditional node-to-linear surface contact algorithms. In our proposed method, contact surfaces were modeled accurately using C1-continuous cubic splines, which interpolate the finite element nodes. In this case, the unit normal vectors are defined uniquely at any point on the contact surfaces. These splines preserve the local deformation of the nodes on each flexible contact surface. Consequently, a consistent linearization of the kinematic contact constraints, based on the spline interpolation, was derived. Moreover, the gap between two contact surfaces was modeled accurately using an efficient surface-to-surface contact search algorithm. Since the continuity of the splines is not affected by the number of nodes, accurate stress distribution can be obtained with less finite elements at the contact surface than that using the traditional linear discretization of the contact surface. Two numerical examples are used to illustrate the advantages of the proposed representation. They show a significant improvement in accuracy compared to traditional piecewise element-based surface interpolation. This approach overcomes the problem of mismatch in a finite element mesh. This is very useful, since most realistic engineering problems involve contact areas that are not known a priori. 相似文献
7.
Mechanical theorem proving in differential geometry 总被引:1,自引:0,他引:1
Hongbo Li 《中国科学A辑(英文版)》1997,40(4):350-356
An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem
proving in local theory of space surfaces in differential geometry. The method has been used to simplify one of Chem’s theorems:
“The non-trivial families of isometric surfaces having the same principal curvatures are W-surfaces.” Some other theorems
are also tested by this method. The proofs are generally simpler than those in differential geometry textbooks.
Project supported partially by the National Natural Science Foundation of China. 相似文献
8.
《Chaos, solitons, and fractals》2001,12(6):1145-1155
A theoretical method for the estimation of the fractal dimensions of the pore surfaces of zeolites is proposed. The method is an analogy to the commonly employed box-counting method and uses imaginary meshes of various sizes (s) to trace the pore surfaces determined by the frameworks of crystalline zeolites. The surfaces formed by the geometrical shapes of the secondary building units of zeolites are taken into account for the calculations performed. The characteristics of the framework structures of the zeolites 13X, 5A and silicalite are determined by the help of the solid models of these zeolites and the total numbers of grid boxes intersecting the surfaces are estimated by using equations proposed in this study. As a result, the fractal dimension values of the zeolites 13X, 5A and silicalite are generally observed to vary in significant amounts with the range of mesh size used, especially for the relatively larger mesh sizes that are close to the sizes of real adsorbates. For these relatively larger mesh sizes, the fractal dimension of silicalite falls below 1.60 while the fractal dimension values of zeolite 13X and 5A tend to rise above 2. The fractal dimension values obtained by the proposed method seem to be consistent with those determined by using experimental adsorption data in their relative magnitudes while the absolute magnitudes may differ due to the different size ranges employed. The results of this study show that fractal dimension values much different from 2 (both higher and lower than 2) may be obtained for crystalline adsorbents, such as zeolites, in ranges of size that are close to those of real adsorbates. 相似文献
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A new mathematical model of the modified bi-Helmholtz equation is proposed for the reconstruction of 3D implicit surfaces using the method of fundamental
solutions. In the algorithm, we also show how to properly determine the parameter
so that the spurious surface can be avoided. The main attraction of the proposed
method is its simplicity. Four examples for the surface reconstruction are presented
to validate the proposed numerical model. 相似文献
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We develop an unconditionally stable direct discretization scheme for solving the phase-field crystal equation on surfaces. The surface is discretized by using an unstructured triangular mesh. Gradient, divergence, and Laplacian operators are defined on triangular meshes. The proposed numerical method is second-order accurate in space and time. At each time step, the proposed computational scheme results in linear elliptic equations to be solved, thus it is easy to implement the algorithm. It is proved that the proposed scheme satisfies a discrete energy-dissipation law. Therefore, it is unconditionally stable. A fast and efficient biconjugate gradients stabilized solver is used to solve the resulting discrete system. Numerical experiments are conducted to demonstrate the performance of the proposed algorithm. 相似文献