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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.


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Journal ArticleDOI
TL;DR: In this article, a method is developed to systematically remove and reintroduce low density elements from and into the finite element mesh on which the structural topology optimization problem is defined, and the material density field which defines the topology and the local stiffness of the structure is optimally distributed via non-linear programming techniques.
Abstract: A method is developed to systematically remove and reintroduce low density elements from and into the finite element mesh on which the structural topology optimization problem is defined. The material density field which defines the topology and the local ‘stiffness’ of the structure is optimally distributed via non-linear programming techniques. To prevent elements from having zero stiffness, an arbitrarily small lower bound on the material density is typically imposed to ensure that the global stiffness matrix does not become singular. While this approach works well for most minimum compliance problems, the presence of low density elements can cause computational problems, particularly in structures that exhibit geometric non-linearities, e.g. in compliant mechanisms. To resolve this problem, a systematic approach for removing and reintroducing low density elements is presented, and the substantial performance improvements both in design and computational efficiency of the method over current methods are discussed. Several structures and compliant mechanisms are designed to demonstrate the method. Copyright © 2003 John Wiley & Sons, Ltd.

196 citations

Journal ArticleDOI
J. Loncaric1
01 Dec 1987
TL;DR: These results, obtained by using a Lie group approach, also extend the concept of the remote center of stiffness to generic generalized springs.
Abstract: A generalized spring associates potential energy with each position and orientation of a rigid body. The stiffness of such a spring can be represented by a 6 × 6 symmetric matrix. This matrix can be brought to a normal form by a particular choice of the coordinate frame. Analogous but independent results hold for compliance matrices. These results, obtained by using a Lie group approach, also extend the concept of the remote center of stiffness to generic generalized springs.

192 citations

Journal ArticleDOI
TL;DR: In this article, the dynamic stiffness matrix of a uniform rotating Bernoulli-Euler beam is derived using the Frobenius method of solution in power series, which includes the presence of an axial force at the outboard end of the beam in addition to the usual centrifugal force arising from the rotational motion.

188 citations

Journal ArticleDOI
TL;DR: In this paper, the stiffness characteristics of a three-prismatic-universal-universal (3-PUU) translational parallel kinematic machine (PKM) are derived intuitively based upon an alternative approach considering actuations and constraints, and the compliances subject to both actuators and legs are involved in the stiffness model.

186 citations

Journal ArticleDOI
TL;DR: In this article, an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle is presented.
Abstract: An element stiffness matrix can be derived by the conventional potential energy principle and, indirectly, also by generalized variational principles, such as the Hu-Washizu principle and the Hellinger-Reissner principle. The present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle. It is found that the resulting scheme is equivalent to that considered by Tong (1982) for the construction of hybrid stress elements. In Tong's scheme the inversion of a large flexibility matrix can be avoided. It is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the Hellinger-Reissner principle and the Hu-Washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method.

181 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202334
202270
202123
202022
201930
201842