| 1. |
- Eriksson, Anders, 1953-
(författare)
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Derivatives of tangential stiffness matrices for equilibrium path descriptions
- 1991
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 32:5, s. 1093-1113
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Tidskriftsartikel (refereegranskat)abstract
- The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non-linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step-wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post-bifurcation behaviour. For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.
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| 2. |
- Eriksson, Anders, 1953-
(författare)
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On improved predictions for structural equilibrium path evaluations
- 1993
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 36:2, s. 201-220
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Tidskriftsartikel (refereegranskat)abstract
- The paper describes how several procedures for higher-order predictions have been introduced in order to improve the convergence speed in a general finite element program for non-linear structural analysis. In addition to higher-order Taylor expansions earlier discussed, Lagrangian extrapolations and some methods commonly used for the integration of initial value problems have been introduced. The methods are used for improved predictions in the stepwise solution of equilibrium states and for accurate descriptions of the initial post-bifurcation behaviour. They are used in a general solution algorithm, based on a parameter formulation. The methods are discussed in the light of the strategies for re-creation of the tangential stiffness matrix, used for equilibrium iterations. Numerical examples, exhibiting different limit and bifurcation behaviours for trusses, frames and shells, are used to evaluate the numerical properties and efficiencies of the methods. The paper concludes that the overall efficiency in the algorithm can be improved by introduction of more accurate predictions than the standard Euler prediction. In terms of reliability combined with efficiency, an implicit generalized Simpson method is the preferred method.
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| 3. |
- Johnsson, Lennart, et al.
(författare)
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Data Structures and Algorithms for the Finite Element Method on a Data Parallel Supercomputer
- 1990
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 29:4, s. 881-908
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Tidskriftsartikel (refereegranskat)abstract
- This article describes a formulation of the finite element method and its implementation on a data parallel computing system. The Connection Machine® system, CM-2, has been used as the model architecture. Data structures, storage requirements, communication and parallel arithmetic complexity are analysed in detail for the cases when a processor represents an unassembled finite element and when a processor is assigned to an unassembled nodal point. Data parallel algorithms for the grid generation, the evaluation of the elemental stiffness matrices and for the iterative solution of the linear system are presented. The algorithm for evaluating the elemental stiffness matrices computes the matrix elements concurrently without communication. This concurrency is in addition to the inherent parallelism present among different finite elements. A conjugate gradient solver with diagonal pre-conditioner is used for the solution of the resulting linear system. Results from an implementation of the three-dimensional finite element method based on Lagrange elements are reported. For single-precision floating-point operations, the measured peak performance is approximately 2·4 G flops s−1 for evaluating the elemental stiffness matrices and approximately 850 M flops s−1 for the conjugate gradient solver. On a Connection Machine system with 16K physical processors, the time per conjugate gradient iteration for an application with 400 000 degrees of freedom is approximately 0·13 s for double-precision floating-point operations.
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| 4. |
- Kjellmert, Bo
(författare)
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Comparative study of the behaviour of a direct solver and a preconditioned iterative solver for the equations arising from the discretization by Chebyshev collocation of a second-order partial differential equation on a square
- 1991
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 32:1, s. 527-539
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Tidskriftsartikel (refereegranskat)abstract
- The behaviour is compared of two solvers for the discrete equations arising from the discretization using Chebyshev collocation of a second-order linear partial differential equation on a square. The alternative solvers considered are a direct solver and an iterative solver based on preconditioning with the matrix arising from finite-difference discretization of the governing equation. The total error of the collocation derivatives and the separate contributions from round-off and discretization error are examined. The efficiency of the two solvers is compared. The iterative solver is more efficient than the direct solver on fine grids for equations similar to the Poisson equation, provided that there are Dirichlet boundary conditions on at least three of the sides of the square.
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| 5. |
- Larsson, Ragnar, et al.
(författare)
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Discontinuos Displacement Apprixamation for capturing Plastic Loacalization
- 1993
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 36:12, s. 2087-2105
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Tidskriftsartikel (refereegranskat)abstract
- It is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by-product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post-peak response (in accordance with non-linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.
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| 6. |
- Oldenburg, Mats, et al.
(författare)
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Position code algorithm for contact searching
- 1994
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 37:3, s. 359-386
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Tidskriftsartikel (refereegranskat)abstract
- A new global search method for general contact systems is developed and implemented in the DYNA3D program, along with a recent contact interface algorithm. The concept of `position codes' for efficient global contact searching is presented. With the position code algorithm, the problem of sorting and searching in three dimensions is transformed to a process of sorting and searching within a one-dimensional array. The cost of contact searching is of the order of N log2 N, where N is the number of nodes in the system. The proposed algorithms are uncomplicated and the implementation into any finite element code is straightforward. Numerical experiments are presented in order to examine the behaviour of the algorithms in different aspects.
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| 7. |
- Ristinmaa, Matti, et al.
(författare)
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Exact integration of constitutive equations in elasto-plasticity
- 1993
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 36:15, s. 2525-2544
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Tidskriftsartikel (refereegranskat)abstract
- A unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity, assuming the total strain-rate direction to be constant. This unified approach includes all previous exact integration procedures as special cases and, in addition, some new closed-form solutions are derived for combined kinematic and isotropic hardening. Special emphasis is laid on combined kinematic and isotropic hardening for von Mises' material and on isotropic hardening for Mohr-Coulomb and Tresca materials.
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| 8. |
- Zang, W.L., et al.
(författare)
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Contact Problems Of Kinked Cracks Modeled By A Boundary Integral Method
- 1990
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 29:4, s. 847-860
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Tidskriftsartikel (refereegranskat)abstract
- Based on the integral equation for the resultant forces along a crack, a numerical method is developed for the solution of two dimensional kinked crack problems taking crack contact into account. The method is demonstrated by a consideration of an elastic half-plane containing a piece-wise straight line crack. Two numerical examples are presented and compared to finite element calculations. The numerical results indicate that the present method can be an effective and reliable tool for investigations of kinked crack problems associated with crack contact.
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| 9. |
- Zang, W.L., et al.
(författare)
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Frictional Contact Problems Of Kinked Cracks Modeled By A Boundary Integral Method
- 1991
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 31:3, s. 427-446
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Tidskriftsartikel (refereegranskat)abstract
- A numerical method is presented for the solution of two dimensional crack problems including the effects of crack kinks and frictional contact between crack faces. The method is based on an integral equation for the resultant forces along a crack. Coulomb friction between contacting crack surfaces is taken into account. The numerical implementation is demonstrated by considerations of surface and sub-surface piece-wise straight line cracks in a half-plane. Numerical results are presented to illustrate the efficiency and the reliability of the presented method.
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| 10. |
- Zeng, L.F., et al.
(författare)
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Adaptive finite element procedure for 2D dynamic transient analysis using direct integration
- 1992
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 34:3, s. 997-1014
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Tidskriftsartikel (refereegranskat)abstract
- An adaptive h-version finite element procedure is presented for a 2D elastodynamic transient analysis using direct integration. The procedure modifies the spatial discretization, i.e. the mesh, in time so that the spatial discretization error can be controlled in each time instant. We analyse an a priori error estimate for the total energy which shows that an a posteriori error estimate developed by Zienkiewicz and Zhu for linear elastostatics can reasonably be extended to dynamic transient analysis. For the time integration, both explicit and implicit time integration schemes can be coupled with the procedure. However, the study in this paper is confined to the use of the Newmark scheme. Numerical examples are used to study the performance of the error estimate and to illustrate the adaptive procedure. Obtained numerical results indicate that: (i) the extension of the Zienkiewicz-Zhu estimate to dynamic transient analysis is useful; (ii) the presented adaptive procedure can, in an efficient way, provide a finite element solution with a user-controlled accuracy.
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