摘要:

AbstractIn two‐dimensional penalty finite element analysis of incompressible materials, Q9/3P, the 9‐node quadrilateral with three assumed quasi‐pressure modes, is the most popular element not bothered by spurious pressure. In constructing the penalty matrix of Q9/3P, it is necessary to form a 3×18 matrix and a 3×3 symmetric matrix. The inverse of the symmetric matrix is then post‐ and pre‐multiplied by the 3×18 matrix and its transpose, respectively. By employing a rank subtraction technique, a new and more efficient implementation scheme is devised for the penalty matrix. Same as the conventional Q9 element, when Q9/3P is fully integrated, it becomes expensive and too stiff. On the other hand, there are two spurious kinematic modes should the element be sub‐integrated. In the proposed Q9/3P element, the two mechanisms will be annihilated by judiciously chosen higher‐order assumed stress modes in conjunction with a modified Hellinger‐Reissner functional. It will be demonstrated that the element is of good accuracy a

ISSN:0029-5981    

DOI:10.1002/nme.1620382302

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA methodology for analysing the numerical errors generated by schemes using high‐order approximation is presented. Based on Fourier analysis, this methodology is illustrated through the study of the θ‐weighting Taylor–Galerkin finite element model applied to an unsteady one‐dimension advection problem with quadratic elements. Results show that the dissipation and dispersion errors may be computed by considering simultaneously the so‐called physical and computational modes and then, contrarily to what is shown when linear approximation is considered, these errors present a transient behaviour. Moreover, it appears that the errors computed at the end node and at the middle node present in general a different behaviour which in some cases may be opposed to one another. Numerical tests are presented to support the validity of the proposed strategy. We recommend strongly the use of this method for studying the behaviour of numerical schemes based on high‐order ap

ISSN:0029-5981    

DOI:10.1002/nme.1620382303

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA finite element numerical simulation model for the liquid phase electroepitaxial growth process of gallium arsenide is presented. The basic equations obtained from the fundamental principles of electrodynamics of continua, the constitutive equations for the liquid and solid phases derived from a rational thermodynamic theory, and the associated interface and boundary conditions are presented for a two‐dimensional axisymmetric growth cell configuration.The field equations are solved numerically by an adaptive finite element procedure. The effect of moving interfaces is taken into account. Numerical simulations are carried out for different convection levels by changing the value of the gravitational constant. Results show that convection has significant effect on the growth process under normal gravity conditions and results in thickness non‐uniformity of the grown layers. The thickness non‐uniformity leads to curved interfaces of growth and dissolution, which enhance conve

ISSN:0029-5981    

DOI:10.1002/nme.1620382304

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA methodology is presented for enforcing a contact constraint between a viscoplastic workpiece and the tooling which deforms it. The algorithm is based on a consistent penalty approach wherein an elemental discretization permits elimination of contact tractions prior to solution for the velocity field. When written in rate form, the new algorithm allows contact constraints to be embedded in a viscoplastic formulation without altering the structure of the global matrix equation. Examples are presented to illustrate its use in metal forming simulations.

ISSN:0029-5981    

DOI:10.1002/nme.1620382305

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA new finite element, viable for use in the three‐dimensional simulation of transient physical processes with sharply varying solutions, is presented. The element is intended to function in adaptiveh‐refinement schemes as a versatile transition between regions of different refinement levels, ensuring interelement continuity by constructing a piecewise linear solution at the element boundaries, and retaining all degrees of freedom in the solution phase. Construction of the element shape functions is described, and a numerical example is presented which illustrates the advantages of using such an element in an adaptive refinement problem. The new element can be used in moving‐front problems, such as those found in reservoir engineering and groundwater flow applica

ISSN:0029-5981    

DOI:10.1002/nme.1620382306

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this paper we introduce a method to reduce the solution cost for Boundary Element (BE) models fromO(N3)operations toO(N2logN) operations (whereNis the number of elements in the model). Previous attempts to achieve such an improvement in efficiency have been restricted in their applicability to problems with regular geometries defined on a uniform mesh. We have developed the Spectral Multipole Method (SMM) which can be used not only for problems with arbitrary geometries but also with a variety of element types. The memory necessary to store the required influence coefficients for the spectral multipole method isO(N) whereas the memory required for the traditional Boundary Element method isO(N2). We demonstrate the savings in computational speed and fast memory requirements in some numerical examples. We have established that the break‐even point for the method can be as low as 500 elements, which implies that the method is not only suitable for extremely large‐scale problems, but that it also provides a useful bridge between the small‐scale and large‐scale problems. We also demonstrate the performance of the multipole algorithm on the solution of large‐scale granular assembly models. The large‐scale BE capacity provided by this algorithm will not only prove to be useful in large macroscopic models but it will also make it possible to model microscopic damage processes that form the fundamental mechanisms in plastic flow and britt

ISSN:0029-5981    

DOI:10.1002/nme.1620382307

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA design procedure for integrating topological considerations in the framework of structural optimization is presented. The proposed approach is capable of considering multiple load conditions, stress, displacement and local/global buckling constraints, and multiple objective functions in the problem formulation. Further, since the proposed method permits members to be added to or deleted from an existing topology and the topology is not defined by member areas, the difficulty of not being able to reach singular optima is also avoided. These objectives are accomplished using a discrete optimization procedure which uses 0–1 topological variables to optimize alternate designs. Since the topological variables are discrete in nature and the member cross‐sections are assumed to be continuous, the topological optimization problem has mixed discrete‐continuous variables. This non‐linear programming problem is solved using a memory‐based combinatorial optimization technique known as tabu search. Numerical results obtained using tabu search for single and multiobjective topological optimization of truss structures are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that the optimum topologies obtained using tabu search compare favourably, and in some instances, outperform the results obtained using the ground–structure approach. However, this improvement occurs at the expense of a significant increase in computational burden owing to the fact that the proposed approach necessitates that the geometry of each trial topology b

ISSN:0029-5981    

DOI:10.1002/nme.1620382308

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractMost incremental‐iterative methods for tracing the postbuckling paths of structures have failed to achieve convergent solutions when the paths make sharp turns in regions where nearby equilibrium paths exist. This is largely due to the fact that iterations are not performed along a correct direction in these regions. To overcome this issue, two parameters for detecting the change in direction of loading and for guiding the direction of iteration are proposed. Also, a unit conversion factor is introduced into the constraint (arc length) equation to make it physically consistent. With these modifications, the present method is capable of tracing the postbuckling paths of structures with multi‐loops. A two‐member truss well known for its looping characteristics in the post‐buckling response has been solved as an illus

ISSN:0029-5981    

DOI:10.1002/nme.1620382309

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620382310

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620382301

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY