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.

Nonlinear Analytical Modeling and Characteristic Analysis of a Class of Compound Multibeam Parallelogram Mechanisms

Abstract: This paper deals with nonlinear analytical models of a class of compound multi-beam parallelogram mechanisms (CMPMs) along with the static characteristic analysis. The CMPM is composed of multiple compound basic parallelogram mechanisms (CBPMs) in an embedded parallel arrangement. Firstly, nonlinear analytical models for the CBPM are derived using the free-body diagram method through appropriate approximation strategies. The nonlinear analytical models of the CMPM are then derived based on the modeling results of the CBPM. Nonlinear finite element analysis (FEA) comparisons, experimental testing, and detailed stiffness analysis for the CBPM are finally carried out. It is shown that the analytical primary motion model agrees with both the FEA model and the testing result very well but the analytical parasitic motion model deviates from the FEA model over the large primary motion/force. It is also shown from the analytical characteristic analysis that the primary translational stiffness increases with the primary motion but the parasitic motion stiffness decreases with the primary motion, and the stiffness ratio of the parasitic motion stiffness to the primary translation stiffness also decreases with the primary motion. It is found that the larger the beam slenderness ratio is, the larger the stiffness or stiffness ratio is, and the more apparent the change of the stiffness or stiffness ratio is. The varied stiffness ratio indicates the mobility change of the CBPM.

Non-destructive damage evaluation of a structure from limited modal parameters

Abstract: A method to predict structural damage in its location and severity from modal characteristics of the damaged structure is proposed. No a priori knowledge of the modal characteristics of a corresponding baseline structure is required in the proposed formulation. Instead, information on the geometry of the structure which is reflected in its mass and stiffness distribution is needed. From matrix structural analysis, a system of equations is generated which relates the relative change of stiffness of structural members to a load vector generated from modal parameters of the damaged structure. Different solution techniques are suggested to determine the damage from the generated equations. The feasibility of the proposed formulation is demonstrated via a numerical example of a 10-storey building. Further, an error investigation on the error in the damage predictions due to uncertainties in the input data is carried out.

Beam on Elastic Foundation Finite Element

Abstract: A stiffness matrix for a beam on elastic foundation finite element and element load vectors due to concentrated forces, concentrated moments, and linearly distributed forces are developed for plane frame analysis. This element stiffness matrix can be readily adopted for the conventional displacement method. For the force method, an element flexibility matrix and element displacement vectors due to the aforementioned loads are also presented. Whereas most other analyses of a beam on elastic foundation finite element approximate the foundation by discrete springs or by cubic hermitian polynomials, the present stiffness and flexibility matrices are derived from the exact solution of the differential equation. Thus, results of this finite element analysis are exact for Navier and Winkler assumptions. Numerical examples are given to demonstrate the efficiency and simplicity of the element.