摘要:

AbstractA modification of the collocation method for the numerical solution of Cauchy‐type singular integral equations appearing in plane elasticity and, especially, crack problems is proposed. This modification, based on a variable transformation, applies to the case when the unknown function of the singular integral equation behaves likeA(x−c)α+B(x−c)β, where α<0, 0<β − α<1, near an endpoint c of the integration interval. In plane elasticity such a point is either a crack tip or a corner point of the boundary of the elastic medium. Thus the method seems to be quite efficient for the numerical evaluation of generalized stress intensity factors near such points. A successful application of the method to the classical plane elasticity problem of an antiplane shear crack terminating at a bimaterial interface w

ISSN:0029-5981    

DOI:10.1002/nme.1620140702

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractAn updated Lagrangian and a total Lagrangian formulation of a three‐dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are give

ISSN:0029-5981    

DOI:10.1002/nme.1620140703

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractA new numerical method of calculating unsteady‐state heat conduction and thermal stresses by using improved coefficient matrix patterns on the nodal points of a structure is given. Good agreement is obtained between our results and the rigorous results, and this method seems to yield better accuracy than other well‐known approximate methods for two‐dimensional transient thermal stress pro

ISSN:0029-5981    

DOI:10.1002/nme.1620140704

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe homogeneous Dirichlet problem for the biharmonic operator is solved as the variational formulation of two coupled second‐order equations. The discretization by a mixed finite element model results in a set of linear equations whose coefficient matrix is sparse, symmetric but indefinite. We describe a class of preconditioned conjugate gradient methods for the numerical solution of this linear system. The precondition matrices correspond to incomplete factorizations of the coefficient matrix. The numerical results show a low computational complexity in both number of computer operations and demand of storag

ISSN:0029-5981    

DOI:10.1002/nme.1620140705

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractMethods for comparing the accuracy of numerical methods for the solution of parabolic partial differential equations are briefly surveyed. Criteria for a more systematic comparison are proposed and applied to an accuracy comparison of the classical and the modified Saul'yev methods and the Crank–Nicholson method on a simple linear problem. The results obtained, which include observation of the existence of optimal spatial mesh size for the two Saul'yev methods, are discusse

ISSN:0029-5981    

DOI:10.1002/nme.1620140706

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe nonlinear impact of a vehicle against a deformable barrier and its subsequent rebound from that barrier are simulated. A one‐dimensional elastoplastic model represents the vehicle as a series of rod finite elements and the barrier as a single mass, nonlinear spring. The solution procedure utilizes variable time step integration, contains an error control and eliminates numerical instabilities. A limited study assesses the influence of system parameters on both structure and occupants. The chief objective, however, is to establish the feasibility of the proposed treatment of this class of problems. Some results obtained appear, at first, to contradict intuition. It is observed that modelling a deformable barrier as rigid can lead to unconservative results with respect to structural response of the vehicl

ISSN:0029-5981    

DOI:10.1002/nme.1620140707

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe application of finite element methods to parabolic partial differential equations leads to large linear systems of first‐order ordinary differential equations. Very often these systems are stiff and difficulties arise in their numerical solution. We attempt to analyse the problem of how to select numerical methods for the solution of such linear system

ISSN:0029-5981    

DOI:10.1002/nme.1620140708

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractSimilar and similarly oriented CST elements have the same stiffness matrix, and therefore similar shapes generated by the assembly of such elements possess the same stiffness matrix. This property and the matrix condensation technique may be judiciously combined to simplify the study of large structures, which may otherwise incur large core requirements and time and involve the solution of a great number of equations. In this paper the idea is developed to indicate its full potential. In illustration, results from examples on the determination of stresses around a small hole in a large plate are presented.

ISSN:0029-5981    

DOI:10.1002/nme.1620140709

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractA technique for smoothing the transition between structural components modelled with dissimilar finite element meshes is presented. The interface mismatch is assigned a potential of dislocation, which is minimized with respect to selected kinematic parametes of the mating surface. This leads to linear constraints between the caididate representations of the mating surface which essentially dictate a least‐square error in dislocaiton. The constraints are enforced by the Lagrange multiplier or reduced stiffness technique. Numerical results indicate gradual transition in the predicted stresses neighbouring the interface. Existing computer codes which permit multipoint constraint specifications are readily available to implement the techniqu

ISSN:0029-5981    

DOI:10.1002/nme.1620140710

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe decomposition of a block tridiagonal matrix into the product of block lowe and upper matrices is described. The cost of solving a block tridiagonal system of equations is given and compared to profile gaussian elimination. The desirability of a less expensive method is coupled to physical intuition about a common problem of solving a slowly varying sequence of such systems to motivate an iterative method based on residual correction. The method is described and convergence criteria are derived. An expression of the cost is developed and is shown to compare favourably with decomposition in many cases. Problems and advantages in computer implementation of the method are discussed and results of tests of a particular implementation on a well‐known problem are give

ISSN:0029-5981    

DOI:10.1002/nme.1620140711

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY