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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, the motion differential equations of the bi-directional functionally graded Timoshenko beam are established using Hamilton's principle using variable substitution method, and the influence of gradient parameters α, β on the fundamental frequency, mode shape and frequency response function is analyzed through the establishment of the dynamic stiffness matrix of the overall structure.
79 citations
TL;DR: In this paper, an exact finite-layer flexibility matrix is introduced for the analysis of a horizontally layered elastic material and it is shown that this matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite.
Abstract: It is well known that the analysis of a horizontally layered elastic material can be considerably simplified by the introduction of a Fourier or Hankel transform and the application of the finite layer approach. The conventional finite layer (and finite element) stiffness approach breaks down when applied to incompressible materials. In this paper these difficulties are overcome by the introduction of an exact finite layer flexibility matrix. This flexibility matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite for an incompressible material. The method is illustrated by a series of examples drawn from the geotechnical area, where it is observed that many natural and man-made deposits are horizontally layered and where it is necessary to consider incompressible behaviour for undrained conditions. For abstract of part 2 see TRIS no. 378330. (Author/TRRL)
79 citations
TL;DR: In this paper, a comparison of available numerical structural analysis formulations for composite beams with partial shear interaction is presented, which include the finite difference method, the finite element method, and the direct stiffness method.
79 citations
TL;DR: In this article, a linear least squares problem is used to identify the local stiffness of a structure from vibration test data, based on a projection of the experimentally measured flexibility matrix onto the strain energy distribution in local elements or regional superelements.
Abstract: A new method is presented for identifying the local stiffness of a structure from vibration test data. The method is based on a projection of the experimentally measured flexibility matrix onto the strain energy distribution in local elements or regional superelements. Using both a presumed connectivity and a presumed strain energy distribution pattern, the method forms a well-determined linear least squares problem for elemental stiffness matrix eigenvalues. These eigenvalues are directly proportional to the stiffnesses of individual elements or superelements, including the cross-sectional bending stiffnesses of beams, plates, and shells, for example. An important part of the methodology is the formulation of nodal degrees of freedom as functions of the measured sensor degrees of freedom to account for the location offsets which are present in physical sensor measurements. Numerical and experimental results are presented which show the application of the approach to example problems.
79 citations
TL;DR: In this paper, an exact dynamics stiffness matrix is developed and subsequently used for free vibration analysis of a twisted beam whose flexural displacements are coupled in two planes, and the resulting dynamic stiffness matrix was used in connection with the Wittrick-Williams algorithm to compute natural frequencies and mode shapes of a twitched beam with cantilever end condition.
79 citations