| 1. |
- Eriksson, Anders, 1953-
(författare)
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On linear constraints for Newton-Raphson corrections and critical point searches in structural F.E. problems
- 1989
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 28:6, s. 1317-1334
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Tidskriftsartikel (refereegranskat)abstract
- The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non-linear mechanical Finite Element (F.E.) problems. An alternative to the normal two-phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.
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| 2. |
- Eriksson, Anders, 1953-
(författare)
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ON SOME PATH-RELATED MEASURES FOR NON-LINEAR STRUCTURAL F. E. PROBLEMS.
- 1988
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 26:8, s. 1791-1803
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Tidskriftsartikel (refereegranskat)abstract
- In the paper, the solution of a non-linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behavior, guiding the iteration strategy in coming steps. Two path-related stiffness measures are derived, giving information concerning the behavior of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measures.
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| 3. |
- Eriksson, Anders, 1953-
(författare)
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USING EIGENVECTOR PROJECTIONS TO IMPROVE CONVERGENCE IN NON-LINEAR FINITE ELEMENT EQUILIBRIUM ITERATIONS.
- 1987
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 24:3, s. 497-512
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Tidskriftsartikel (refereegranskat)abstract
- In an earlier paper a method for calculation of non-linear structural response was described. A method for selective damping of solution components parallel to critical eigenvectors was proposed, reducing the risk for diverging equilibrium iterations. This method is, in the present paper, shown to be related to the 'dynamic relaxation' approach. The method has been further studied for practical problems, and especially adapted for the analysis of plate buckling. A method for variable damping is proposed, and compared to existing methods. The conclusions are that damping, based on eigenvector projection, is an efficient way to improve the stability in the iterations, and in this an alternative to other methods for choice of optimum corrections in N-R schemes. In the paper, suitable criteria for reformulation of the tangential relation during iterations in a step are also discussed.
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| 4. |
- Johnsson, Lennart, et al.
(författare)
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Experience with the Conjugate Gradient Method for Stress Analysis on a Data Parallel Supercomputer
- 1989
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 27:3, s. 523-546
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Tidskriftsartikel (refereegranskat)abstract
- The storage requirements and performance consequences of a few different data parallel implementations of the finite element method for domains discretized by three-dimensional brick elements are reviewed. Letting a processor represent a nodal point per unassembled finite element yields a concurrency that may be one to two orders of magnitude higher for common elements than if a processor represents an unassembled finite element. The former representation also allows for higher order elements with a limited amount of storage per processor. A totally parallel stiffness matrix generation algorithm is presented. The equilibrium equations are solved by a conjugate gradient method with diagonal scaling. The results from several simulations designed to show the dependence of the number of iterations to convergence upon the Poisson ratio, the finite element discretization and the element order are reported. The domain was discretized by three-dimensional Lagrange elements in all cases. The number of iterations to convergence increases with the Poisson ratio. Increasing the number of elements in one special dimension increases the number of iterations to convergence, linearly. Increasing the element order p in one spatial dimension increases the number of iterations to convergence as pα, where α is 1·4–1·5 for the model problems.
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| 5. |
- Karlsson, Lennart
(författare)
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Numerical analysis of damped transient beam vibrations by use of Fourier transforms
- 1985
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 24:4, s. 683-689
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Tidskriftsartikel (refereegranskat)abstract
- The objective of the present study is to investigate the applicability of the Fourier transform technique to the analysis of vibrating damped beam structures. The practical use of the method is demonstrated by calculating a measure of the noise emitted by a vibrating damped beam. Different distributed Winkler-type foundations are studied as a means of noise reduction in the vibrating damped beam structure. This type of damping can be applied to the drill rods employed in rock drilling
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| 6. |
- Lindgren, Lars-Erik, et al.
(författare)
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Deformations and stresses in welding of shell structures
- 1988
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 25:2, s. 635-655
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Tidskriftsartikel (refereegranskat)abstract
- The simulation of welding of shell structures is investigated in this paper. In order to verify the implementation of the shell element adopted, two different problems were studied. In the first problem the butt-welding of two plates was simulated. In the second problem the butt-welding of a thin-walled pipe was simulated. It is concluded from the analysis of the plate problem that the shell element is quite effective in the membrane state. The comparison between calculated values and experimental values for the residual stress field in the pipe shows that the shell element performs quite well in the analysis of a realistic problem
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| 7. |
- Ottosen, Niels Saabye, et al.
(författare)
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Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour
- 1985
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 21:12, s. 2237-2256
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Tidskriftsartikel (refereegranskat)abstract
- The frequently used subincremental method has so far been based on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic–plastic behaviour and secondary creep is involved. The present paper proposes a nonlinear subincremental method applicable to general elastic–plastic–creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear-approach for elastic–plastic behaviour and when secondary creep is present. It is also linear during step loadings and it becomes increasingly more nonlinear, the more creep hardening deformations dominate the behaviour. A wide range of structures are analysed and the results from both subincremental methods are compared; the nonlinear strategy increases the accuracy by a factor of typically 3–5 without affecting the computer time. Moreover, the implementation of the nonlinear method is extremely simple. The optimum number of substeps in each main step is found to be around 5. For such a choice, the advantage of using the subincremental method as compared to the more conventional solution technique, where only one type of time step is used, is a significant reduction in computer time without, in practice, affecting the accuracy.
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| 8. |
- Runesson, Kenneth, et al.
(författare)
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Numerical technique in plasticity including solution advancement control
- 1986
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 22:3, s. 769-788
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Tidskriftsartikel (refereegranskat)abstract
- Numerical techniques applied to the consistent formulation of plasticity, which is based on convex analysis, are investigated. For each time step the stress is found as the projection in complementary energy of the elastic stress onto the set of plastically admissible stresses, while the velocity field is the extremal of a non-quadratic functional. Explicit formulas for von Mises' yield criterion with mixed hardening are developed and the nonlinear equations arising from finite element discretization are solved, for comparison, by a number of Newton-type iteration procedures with line search and arc-length control. A few numerical examples with proportional and non-proportional loading are analyzed.
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| 9. |
- Samuelsson, A., et al.
(författare)
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Study of the efficiency of iterative methods for linear problems in structural mechanics
- 1986
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 22:1, s. 209-218
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Tidskriftsartikel (refereegranskat)abstract
- The efficiency of iterative methods in linear structural mechanics is studied. The efficiency concerns the calculation time, the numerical accuracy and the core storage needed. We state that iterative methods are effective in connection with hierarchical improvement of a primary approximation. Three iterative methods are studied: the conjugate gradient method preconditioned by a modified incomplete factorization matrix, the same method preconditioned by a matrix obtained from natural factors on elemental level, and a Jacobi integration preconditioned by viscous relaxation split in an element-by-element way. We make comparisons with direct methods, Gaussian elimination and factorization by use of natural factors.
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| 10. |
- Ståhle, P.
(författare)
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Using Elastic Plastic Plane-Stress Fem Programs to Compute Antiplane Strain
- 1986
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 23:10, s. 1847-1856
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Tidskriftsartikel (refereegranskat)abstract
- Elastic—plastic anti‐plane strain problems can be solved by using FEM programs developed for plane stress. The technique does not involve any manipulations with the FEM code, but is merely a matter of specialization and of translation of notation. Two analytically solvable cases are chosen for demonstration.
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