共查询到20条相似文献，搜索用时 0 毫秒
1.
Dustin R. Jantos Klaus Hackl Philipp Junker 《International journal for numerical methods in engineering》2019,117(9):991-1017
In a series of previous works, we established a novel approach to topology optimization for compliance minimization based on thermodynamic principles known from the field of material modeling. Hamilton's principle for dissipative processes directly yields a partial differential equation (referred to as the evolution equation) as an update scheme for the spatial distribution of density mass describing the topology. Consequently, no additional mathematical minimization algorithms are needed. In this article, we introduce a regularization scheme by penalization of the gradient of the spatial distribution of mass density. The parabolic evolution equation (owing to a similar structure to the transient heat-conduction equation) is solved most efficiently by an explicit time discretization. The Laplace operator is discretized via a Taylor series expansion yielding an operator matrix that is constant for the entire optimization process. This method shares some similarities to meshless methods and allows for an accurate application also on unstructured finite element meshes. The minimal size of the structure member can directly be controlled, a priori, by a numerical parameter introduced along with the regularization, similar to classical filter radii. 相似文献
2.
A. Rassineux P. Breitkopf P. Villon 《International journal for numerical methods in engineering》2003,57(3):371-389
We present a method to adapt a tetrahedron mesh together with a surface mesh with respect to a size criterion. The originality of our work lies in the fact that both surface and tetrahedron mesh adaptation are carried out simultaneously and that no CAD is required to adapt the surface mesh. The adaptation procedure consists of splitting or removing interior and surface edges which violate a given size criterion. The enrichment process is based on a bisection technique. In order to guarantee mesh conformity during the refinement process, all possible remeshing configurations of tetrahedra have been examined. Once the tetrahedron mesh has been adapted, surface nodes are projected on a geometrical model. The building of a surface model from discrete data has already been presented in this journal. The method is based on a mesh‐free technique called Hermite Diffuse Interpolation. Surface and volume mesh optimization procedures are carried out during the adaptation and at the end of the process to enhance the mesh. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
3.
Peter Mller Peter Hansbo 《International journal for numerical methods in engineering》1995,38(21):3551-3569
This paper deals with some aspects of unstructured mesh generation in three dimensions by the advancing front technique. In particular, the parameters used in the algorithm are characterized, and strategies that may be used to improve robustness are suggested. We also describe a method whereby structured tetrahedral meshes with exceptionally stretched elements adjacent to boundary surfaces may be produced. The suggested method can be combined with the advancing front concept in a natural way. 相似文献
4.
C. A. Duarte T. J. Liszka W. W. Tworzydlo 《International journal for numerical methods in engineering》2007,69(11):2409-2440
In spite of significant advancements in automatic mesh generation during the past decade, the construction of quality finite element discretizations on complex three‐dimensional domains is still a difficult and time demanding task. In this paper, the partition of unity framework used in the generalized finite element method (GFEM) is exploited to create a very robust and flexible method capable of using meshes that are unacceptable for the finite element method, while retaining its accuracy and computational efficiency. This is accomplished not by changing the mesh but instead by clustering groups of nodes and elements. The clusters define a modified finite element partition of unity that is constant over part of the clusters. This so‐called clustered partition of unity is then enriched to the desired order using the framework of the GFEM. The proposed generalized finite element method can correctly and efficiently deal with: (i) elements with negative Jacobian; (ii) excessively fine meshes created by automatic mesh generators; (iii) meshes consisting of several sub‐domains with non‐matching interfaces. Under such relaxed requirements for an acceptable mesh, and for correctly defined geometries, today's automated tetrahedral mesh generators can practically guarantee successful volume meshing that can be entirely hidden from the user. A detailed technical discussion of the proposed generalized finite element method with clustering along with numerical experiments and some implementation details are presented. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
5.
A. Rassineux 《International journal for numerical methods in engineering》1998,41(4):651-674
An algorithm for tetrahedron mesh generation and optimization with respect to a shape and a size criterion is presented. A well distributed set of nodes is first generated by an octree method, and the set is then triangulated. The advancing front technique is used to mesh the whole volume. Emphasis has been placed on management of the front. The method involves priority construction of enhanced quality tetrahedra. Each face is assigned to a front corresponding to the quality of the best tetrahedron which can be constructed. Elements are destroyed in the case of non-convergence. Optimization procedures make local use of the algorithm used to mesh the complete model. Industrial examples of relatively complex volumes are given, demonstrating that a high quality and optimized mesh can be obtained by the proposed method. © 1998 John Wiley & Sons, Ltd. 相似文献
6.
A new unstructured mesh coarsening algorithm has been developed for use in conjunction with multilevel methods. The algorithm preserves geometrical and topological features of the domain, and retains a maximal independent set of interior vertices to produce good coarse mesh quality. In anisotropic meshes, vertex selection is designed to retain the structure of the anisotropic mesh while reducing cell aspect ratio. Vertices are removed incrementally by contracting edges to zero length. Each vertex is removed by contracting the edge that maximizes the minimum sine of the dihedral angles of cells affected by the edge contraction. Rarely, a vertex slated for removal from the mesh cannot be removed; the success rate for vertex removal is typically 99.9% or more. For two‐dimensional meshes, both isotropic and anisotropic, the new approach is an unqualified success, removing all rejected vertices and producing output meshes of high quality; mesh quality degrades only when most vertices lie on the boundary. Three‐dimensional isotropic meshes are also coarsened successfully, provided that there is no difficulty distinguishing corners in the geometry from coarsely‐resolved curved surfaces; sophisticated discrete computational geometry techniques appear necessary to make that distinction. Three‐dimensional anisotropic cases are still problematic because of tight constraints on legal mesh connectivity. More work is required to either improve edge contraction choices or to develop an alternative strategy for mesh coarsening for three‐dimensional anisotropic meshes. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
7.
Matthew L. Staten Robert A. Kerr Steven J. Owen Ted D. Blacker Marco Stupazzini Kenji Shimada 《International journal for numerical methods in engineering》2010,81(2):135-171
The generation of all‐hexahedral finite element meshes has been an area of ongoing research for the past two decades and remains an open problem. Unconstrained plastering is a new method for generating all‐hexahedral finite element meshes on arbitrary volumetric geometries. Starting from an unmeshed volume boundary, unconstrained plastering generates the interior mesh topology without the constraints of a pre‐defined boundary mesh. Using advancing fronts, unconstrained plastering forms partially defined hexahedral dual sheets by decomposing the geometry into simple shapes, each of which can be meshed with simple meshing primitives. By breaking from the tradition of previous advancing‐front algorithms, which start from pre‐meshed boundary surfaces, unconstrained plastering demonstrates that for the tested geometries, high quality, boundary aligned, orientation insensitive, all‐hexahedral meshes can be generated automatically without pre‐meshing the boundary. Examples are given for meshes from both solid mechanics and geotechnical applications. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
8.
Chongbin Zhao B. E. Hobbs H. B. Mühlhaus A. Ord 《International journal for numerical methods in engineering》1999,45(10):1509-1526
To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point‐searching algorithm for solution interpolation in unstructured meshes consisting of 4‐node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point‐searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 to mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co‐ordinates of any point in a four‐node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point‐searching algorithm. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
9.
Gregory J. Wagner Wing Kam Liu 《International journal for numerical methods in engineering》2000,47(8):1367-1379
Collocation methods for applying essential boundary conditions are defined as those methods in which conditions are enforced exactly at a discrete set of boundary nodes. In mesh‐free methods, this is usually accomplished by replacing rows of the matrix equations which result from discretization of the weak form with equations which ensure the enforcement of boundary conditions. In this paper, an inconsistency in this method is pointed out, and a correction is derived. Numerical test are done on one‐ and two‐dimensional equations; it is shown that convergence rates decrease with the use of the invalid traditional collocation and are restored with the corrected method. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
10.
K. WILLCOX J. PERAIRE 《International journal for numerical methods in engineering》1997,40(13):2413-2431
A strategy for computing aeroelastic solutions is proposed. An implicit LU factorization scheme for solving the time-dependent Euler equations on unstructured triangular meshes is presented and coupled with a typical section aeroelastic wing model. Efficiency is improved by coupling the LU factorization scheme with a GMRES algorithm. In this case the LU scheme plays the role of a preconditioner. The fluid and structural models are simultaneously integrated in time in a fully coupled manner. The response of a structural section in different flow regimes is determined and flutter boundaries are computed. In the transonic regime and beyond the region of linear stability, the section is found to exhibit limit cycle behaviour. © 1997 by John Wiley & Sons, Ltd. 相似文献
11.
Daniel W. Zaide Carl F. Ollivier‐Gooch 《International journal for numerical methods in engineering》2016,106(6):484-500
In this work, a new method for inserting a surface as an internal boundary into an existing unstructured tetrahedral mesh is developed. The surface is discretized by initially placing vertices on its bounding curves, defining a length scale at every location on each boundary curve based on the local underlying mesh, and equidistributing length scale along these curves between vertices. The surface is then sampled based on this boundary discretization, resulting in a surface mesh spaced in a way that is consistent with the initial mesh. The new points are then inserted into the mesh, and local refinement is performed, resulting in a final mesh containing a representation of the surface while preserving mesh quality. The advantage of this algorithm over generating a new mesh from scratch is in allowing for the majority of existing simulation data to be preserved and not have to be interpolated onto the new mesh. This algorithm is demonstrated in two and three dimensions on problems with and without intersections with existing internal boundaries. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
12.
Marcio Arêdes Martins Leandro Soares Oliveira Ramn Molina Valle 《International journal for numerical methods in engineering》2004,61(10):1625-1643
This paper presents a numerical study of thermal injury in teeth, caused both by convective heating, due to drinking of hot beverage and mastication of foods, and by laser irradiation in dental treatment. The numerical study employs an adaptive finite volume method on unstructured triangular meshes to solve the governing equations. An adaptive time stepping methodology was also used in order to control the solution error. Adaptive methodologies are adequate to solve such problems since steep gradients will develop at specific locations in the domain of study. The convective heating results were compared to experimental data available in the literature. Laser treatment results are in agreement to the temperature increasing observed in literature. The simulation results demonstrate that both the error estimate and adaptive methodology herein proposed are suitable and reliable for the controlled solution of parabolic problems. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
13.
Jacob Waltz 《International journal for numerical methods in engineering》2002,54(7):945-963
A set of derived data structure algorithms for unstructured finite element meshes is presented. Both serial and parallel algorithms are described for each data structure. Colouring groups for the elements are used to facilitate parallelization on shared memory architectures. Scaling studies indicate that the parallel algorithms are most efficient when the number of elements per processor is on the order of 106 or higher, and overall efficiencies of 60–70% are achieved down to 0.5×106 elements per processor. Although the meshes under consideration are tetrahedral, the algorithms are general in nature and can be extended to arbitrary element types with minimal effort. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
14.
Sergio R. Idelsohn Eugenio Oate Carlos Sacco 《International journal for numerical methods in engineering》1999,45(5):503-528
An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes flow as for the free‐surface boundary problem. The incompressible flow equations are solved via a fractional step method whereas the non‐linear free‐surface equation is solved via a reference surface which allows fixed and moving meshes. A new non‐structured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
15.
Serge Dumont Olivier Goubet Tuong Ha‐Duong Pierre Villon 《International journal for numerical methods in engineering》2006,67(7):989-1011
We perform here some meshfree methods to inhomogeneous Laplace equations. We prove the efficiency of those methods compared with classical ones, for one‐ or two‐dimensional case for numerics, and for one‐dimensional for theoretical results. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Carlos Zuppa Alberto Cardona 《International journal for numerical methods in engineering》2003,57(4):509-536
This paper deals with the use of the local optimal point interpolating (LOPI) formula in solving partial differential equations (PDEs) with a collocation method. LOPI is an interpolating formula constructed by localization of optimal point interpolation formulas that reproduces polynomials and verifies the delta Kronecker property. This scheme results in a truly meshless method that produces high quality output and accurate solutions. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
19.
In this article, the static and free vibration analysis of three-layer composite shells is performed by radial basis functions collocation, according to a new layerwise theory that considers independent layer rotations, accounting for through-the-thickness deformation by considering a linear evolution of all displacements with each layer thickness coordinate. The equations of motion and the boundary conditions are obtained by the Carrera’s Unified Formulation, and further interpolated by collocation with radial basis functions. 相似文献
20.
Arash Yavari Ali Kaveh Shahram Sarkani Hosein Ali Rahimi Bondarabady 《International journal for numerical methods in engineering》2001,52(9):921-938
The meshless element‐free Galerkin method (EFGM) is considered and compared to the finite‐element method (FEM). In particular, topological aspects of meshless methods as the nodal connectivity and invertibility of matrices are studied and compared to those of the FE method. We define four associated graphs for meshless discretizations of EFGM and investigate their connectivity. The ways that the associated graphs for coupled FE‐EFG models might be defined are recommended. The associated graphs are used for nodal ordering of meshless models in order to reduce the bandwidth, profile, maximum frontwidth, and root‐mean‐square wavefront of the corresponding matrices. Finally, the associated graphs are numerically compared. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献