Direct stiffness method

About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.

Direct Least-Squares Formulation of a Stiffness Adjustment Method

Abstract: A direct least-squares formulation of the stiffness matrix adjustment method known as the KMA method (Kabe, A. M., Stiffness Matrix Adjustment Using Mode Data, AIAA Journal, Vol. 23, No. 9, 1985, pp. 1431-1436) is presented. The KMA method belongs to a class of procedures that refine dynamic models using test-measured modes and structural connectivity. Viewed as a constrained minimization problem, most of these methods have applied Lagrange multiplier techniques in their development. It is shown that these two approaches result in linear systems of equations that are algebraically equivalent and therefore have identical solutions. By virtue of this equivalence, the direct least-squares formulation of the KMA method is shown to be equivalent to its original Lagrange multiplier formulation. The direct least-squares versions of other model refinement methods that preserve structural connectivity are also discussed. In this respect, this approach provides a rigorous framework for unifying these optimal update procedures and indicates how their solutions should compare. Numerical results are presented that illustrate the equivalence between the two formulations and also the conditions under which the various methods yield identical solutions. The results also indicate that because of improved numerical conditioning, the direct least-squares approach yields more accurate computational solutions and generally requires less computer storage than methods that were developed using Lagrange multipliers.

Accelerated initial stiffness schemes for elastoplasticity

Abstract: Iterative methods for the solution of non-linear finite element equations are generally based on variants of the Newton–Raphson method. When they are stable, full Newton–Raphson schemes usually converge rapidly but may be expensive for some types of problems (for example, when the tangent stiffness matrix is unsymmetric). Initial stiffness schemes, on the other hand, are extremely robust but may require large numbers of iterations for cases where the plastic zone is extensive. In most geomechanics applications it is generally preferable to use a tangent stiffness scheme, but there are situations in which initial stiffness schemes are very useful. These situations include problems where a nonassociated flow rule is used or where the zone of plastic yielding is highly localized. This paper surveys the performance of several single-parameter techniques for accelerating the convergence of the initial stiffness scheme. Some simple but effective modifications to these procedures are also proposed. In particular, a modified version of Thomas' acceleration scheme is developed which has a good rate of convergence. Previously published results on the performance of various acceleration algorithms for initial stiffness iteration are rare and have been restricted to relatively simple yield criteria and simple problems. In this study, detailed numerical results are presented for the expansion of a thick cylinder, the collapse of a rigid strip footing, and the failure of a vertical cut. These analyses use the Mohr–Coulomb and Tresca yield criteria which are popular in soil mechanics. Copyright © 2000 John Wiley & Sons, Ltd.

Theoretical aspects of the internal element connectivity parameterization approach for topology optimization

Abstract: The internal element connectivity parameterization (I-ECP) method is an alternative approach to overcome numerical instabilities associated with low-stiffness element states in non-linear problems. In I-ECP, elements are connected by zero-length links while their link stiffness values are varied. Therefore, it is important to interpolate link stiffness properly to obtain stably converging results. The main objective of this work is two-fold (1) the investigation of the relationship between the link stiffness and the stiffness of a domain-discretizing patch by using a discrete model and a homogenized model and (2) the suggestion of link stiffness interpolation functions. The effects of link stiffness penalization on solution convergence are then tested with several numerical examples. The developed homogenized I-ECP model can also be used to physically interpret an intermediate design variable state.

Exact dynamic stiffness for axial-torsional buckling of structural frames

Abstract: A dynamic axial-torsion buckling theory is proposed for analysis in structural mechanics. Second order effects of the axial force and torque are considered. The consistent natural boundary moments and forces are given to ensure the symmetry of the dynamic stiffness matrix in fulfilling the requirement of the reciprocal theorem. The exact dynamic stiffness matrix is obtained for the first time using power series expansion. Generally distributed axial force can be analyzed without difficulty. It is pointed out that non-uniform sections may not be effectively analyzed due to the convergent problem. The interaction diagrams due to vibration frequency, axial force and torque are studied in details.

Damage localization in reinforced concrete beams by dynamic stiffness determination

Abstract: In the framework of developing a non-destructive vibration testing method for monitoring the structural integrity of constructions in civil engineering, it is important to be able to determine the dynamic stiffness in each section of the structure from measured modal characteristics. From the dynamic stiffnesses, one obtains directly an idea of the extension of the cracked zones in the structure. In an experimental program, a concrete beam of 6 meter length is subjected to an increasing static load to introduce cracks. After each static preload the beam is tested dynamically in a free-free set-up. The change in modal parameters is then translated into damage in the beam. The technique to predict the damage location and intensity that will be presented in the paper, is a direct stiffness derivation from measured modal displacement derivatives. Using the bending modes, the dynamic bending stiffness can be derived from modal curvatures. Using the torsional modes, the dynamic torsion stiffness can be derived from modal torsion rates.