摘要:

AbstractThe application of a four‐parameter generalized midpoint integration method to small‐displacement elastoplastic dynamic problems is considered. The integration of the governing relations over a time step is formulated as a non‐linear algebraic problem (finite‐step problem) by making use of generalized variables finite element modelling. Uniqueness and an extremum characterization of the solution of the finite‐step problem are discussed. Sufficient conditions for convergence of various iterative algorithms, including Newton‐Raphson, are given. The B‐stability of the proposed procedur

ISSN:0029-5981    

DOI:10.1002/nme.1620360302

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA new solution technique has been developed to calculate the frequency shifts arising from mechanical stresses in the case of quartz resonators. This solution technique utilizes finite element analysis as an initial step to calculate mechanical stress distributions in quartz resonators. Output from the finite element solution is used in a recently developed program to calculate resonator frequency shifts as the final step. Frequency shifts are calculated via numerical integration of the perturbation integral derived by Tiersten.36The solution technique is general in that any combination of mount and resonator geometries may be modelled. Any crystallographic orientation may be chosen and any load or combination of loads may be applied to the resonator. The frequency perturbation calculation includes movement of the mode to any position in the general vicinity of the resonator centre. Experimental results for AT‐ and SC‐cut quartz resonators subjected to diametric forces and inertial loading verify the accuracy of frequency shifts calculated using the new solution techni

ISSN:0029-5981    

DOI:10.1002/nme.1620360303

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt is proposed. The boundary‐fitted co‐ordinate system is applied to a treatment for the moving solid‐liquid interface in cylindrical co‐ordinates with a symmetry axis. An alternating‐direction‐implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples

ISSN:0029-5981    

DOI:10.1002/nme.1620360304

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractIn this paper, two finite‐element‐based schemes for second‐order shape sensitivity analysis are presented. In the first formulation, the AV‐DD method, the first‐order shape sensitivity equation is derived and expressed in terms of state and adjoint variables. The resultant equation is then directly differentiated to obtain the second‐order shape sensitivity equation. In the second formulation, the DD‐AV method, the functional of concern is differentiated twice to yield the second‐order sensitivity equation in which the second‐order shape derivatives can be eliminated by introducing a proper adjoint equation. A thermal fin problem and a thermal insulation layer problem have been studied to validate the proposed schemes. It is shown that both methods yield identical results, though the DD‐AV method is computation

ISSN:0029-5981    

DOI:10.1002/nme.1620360305

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractTime‐harmonic elastic wave scattering problems such as those encountered in ultrasonic non destructive evaluation are solved by the boundary element method (BEM). Selected results for spherical and spheroidal shaped voids and inclusions are compared with analytical and other numerical solutions. Results for ellipsoids, which require a full three‐dimensional formulation, are provided as a benchmark for comparison when other numerical methods would be developed for this problem class in the future. The modelling of cracklike defects with this formulation is discussed. Recent theoretical findings regarding the fictitious eigenfrequency difficulty (FED) are confirmed by a numerical st

ISSN:0029-5981    

DOI:10.1002/nme.1620360306

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractWe investigate the effect of the ordering of the blocks of unknowns on the rate of convergence of a preconditioned non‐linear GMRES algorithm, for solving the Navier‐Stokes equations for compressible flows, using finite element methods on unstructured grids. The GMRES algorithm is preconditioned by an incomplete LDU block factorization of the Jacobian matrix associated with the non‐linear problem to solve. We examine a wide range of ordering methods including minimum degree, (reverse) Cuthill‐McKee and snake, and consider preconditionings without fill‐in. We show empirically that there can be a significant difference in the number of iterations required by the preconditioned non‐linear GMRES method and suggest a criterion for choosing a good ordering algorithm, according to the problem to solve.We also consider the effect of orderings when an incomplete factorization which allows some fill‐in is performed. We consider the effect of automatically controlling the sparsity of the incomplete factorization through the level of fill‐in.Finally, following the principal ideas of non‐linear GMRES algorithm, we suggest other inexa

ISSN:0029-5981    

DOI:10.1002/nme.1620360307

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA simple algorithm is developed for adaptive and automatichrefinement of two‐dimensional triangular finite element meshes. The algorithm is based on an element refinement ratio that can be calculated from ana posteriorierror indicator. The element subdivision algorithm is robust and recursive. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several example problems are presented to illustrate the utility of the approac

ISSN:0029-5981    

DOI:10.1002/nme.1620360308

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA commonly adopted procedure to solve a structural optimum design problem is to improve the design iteratively by solving a sequence of simpler problems, where each of these is obtained as an approximation of the original problem. Considering structures with linear response, this procedure works very well and can be implemented quite straightforwardly. However, considering structures with non‐linear response, the situation is more sophisticated since structural stability properties have to be taken into account.The paper presents an approach to optimal design of statically loaded structures with non‐linear response. It is proposed to replace the original problem with a sequence of similar problems from which corresponding approximate problems can easily be obtained. These similar problems additionally contain an estimation of the critical load constraint while other constraints are imposed at some properly chosen load level, which is lower or at most equal to the critical load level. By this approach, the structural stability requirements are taken into account in an effective manner. The efficiency is illustrated with several examples involving kinematic as well as material non‐linear ef

ISSN:0029-5981    

DOI:10.1002/nme.1620360309

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA method for the direct computation of mean values and variances of the temperature in conduction‐heated objects with random variable thermophysical properties is presented. This method is based on a Taylor expansion of the finite element formulation of the heat conduction equation and offers a powerful alternative to the computationally expensive Monte Carlo method. Both steady‐state and transient problems are considered. Some example problems are solved and the results discussed. The simulations indicate that the variability of the thermophysical properties may cause a considerable variability of the temperature within the heated object. This may have important consequences on the design of heating operations in food process engineer

ISSN:0029-5981    

DOI:10.1002/nme.1620360310

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620360311

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY