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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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TL;DR: In this article, an augmentation technique is proposed which takes into account micro-mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase.
Abstract: The detailed discretization of contact zones with contact stiffness based on real physical characteristics of contact surfaces can produce stiffness terms which induce ill-conditioning of the global stiffness matrix. Moreover the consistent treatment of frictional behaviour generates non-symmetric tangent stiffness matrices due to the non-associativity of the slip phase. Other non-symmetries are due to the coupling terms and to the dependencies on various parameters that can be involved. To overcome these difficulties almost consistent techniques based on two-step algorithms have been proposed in the past. Here an augmentation technique is proposed which takes into account micro-mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase.
82 citations
TL;DR: In this paper, a method of modeling the damping matrix of a structure from incomplete experimental data combined with a reasonable representation of the mass and stiffness matrices developed by finite element methods and reduced by standard model reduction techniques is presented.
Abstract: This work provides a method of modeling the damping matrix of a structure from incomplete experimental data combined with a reasonable representation of the mass and stiffness matrices developed by finite element methods and reduced by standard model reduction techniques. The proposed technique uses the reduced mass and stiffness matrices and the experimentally obtained eigenvalues and eigenvectors in a weighted least squares or a speudo-inverse scheme
82 citations
TL;DR: In this paper, a direct method using a strain energy-based RVE-procedure was proposed for the determination of the effective plate stiffness matrix for composite shells with microheterogeneous layers.
Abstract: The present study is concerned with the numerical determination of the effective plate stiffness matrix for composite shells with microheterogeneous layers. Contrary to the standard two-step procedure, where the effective plate or shell stiffness matrix is derived by a projection of the effective elasticity tensor onto the plate or shell reference surface, a direct method is proposed. This method uses a strain energy based RVE-procedure which assumes mechanical equivalence of a representative volume element for the given microstructure and a corresponding plate element if the strain energy in both elements is equal, provided that the effective deformation is equal in an average sense. In parametric studies concerning sandwich plates with hexagonal honeycomb cores, it is observed that the direct method and the two-step procedure are equivalent for the determination of the in-plane and the transverse shear properties while a significant deviation of the results obtained by both methods is found in case of the effective bending properties.
82 citations
TL;DR: In this article, an energy measure of discretization error was proposed for finite element mesh refinement in the analysis of structural continua, based on the strain energy contributions by the admissible displacement response modes of an element.
Abstract: This paper proposes an energy measure of discretization error and examines its use for finite element mesh refinement in the analysis of structural continua.
The measure is based on the strain energy contributions by the admissible displacement response modes of an element. An element energy differential is obtained by separating the energy contribution due to the higher displacement modes. This measure is suitable for use with all element types based on the direct stiffness method.
The paper presents results of membrane, plate and shell analyses using the measure. It compares sequences of analysis with successively improved meshes to explore the quality of the measure. It concludes that the element energy difference provides a quantitative measure of the efficiency of a given mesh and a qualitative measure which is useful for selecting further mesh refinements, when necessary.
80 citations
TL;DR: This work provides a simple technique for computing the member stiffness in many types of bolted connections by performing finite element analyses for joints having a range of materials and geometries.
Abstract: The member stiffness in a bolted connection has a direct influence upon safe design with regard to both static and fatigue loading, as well as in the prevention of separation in the connection This work provides a simple technique for computing the member stiffness in many types of bolted connections Finite element analyses are performed for joints having a range of materials and geometries, and the results are generalized by nondimensionalization An exponential expression for the stiffness is determined, and the results are compared with those of some of the techniques currently used
79 citations