On improved predictions for structural equilibrium path evaluations

• 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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

Nyckelord

Algorithms

Boundary value problems

Computational methods

Convergence of numerical methods

Finite element method

Integration

Iterative methods

Nonlinear equations

Shells (structures)

Structural frames

Trusses

Equilibrium states

Lagrangian extrapolation

Parameter formulation

Post bifurcation behaviour

Stepwise solution

Tangential stiffness matrix

Structural analysis

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