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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: The finite element method has been demonstrated to provide an effective means for the analysis of two-dimensional elastic continua as mentioned in this paper, and the method is applied to a special class of twodimensional system: the axially symmetric elastic solid.
Abstract: The finite element method has been demonstrated to provide an effective means for the analysis of two-dimensional elastic continua. In this paper, the method is applied to a special class of two-dimensional system: The axially symmetric elastic solid. The procedure is identical with that used in plane stress analysis; it is merely necessary to develop special stiffness matrices for the axi-symmetric finite element. In the present development, axi-symmetric elements of triangular cross section are considered (forming complete rings in plan view). The procedure for evaluating the element stiffness is summarized, and the modifications required to adapt a finite element plane stress digital computer program for the treatment of axi-symmetric systems are cited. Results of several example analyses are presented; the solution of the Boussinesq problem, a concentrated load applied to an elastic half-space, demonstrates the accuracy of results that may be obtained.

47 citations

Journal ArticleDOI
R T Severn1
TL;DR: In this article, the stiffness matrix is obtained on the basis of stress assumption, rather than the more usual displacement assumption, and an erroneous addition of the shear-deflection terms to the bending terms can be made if an apparently straightforward approach is utilized.
Abstract: Shear-deflection terms arise naturally in a finite beam element in bending if the stiffness matrix is obtained on the basis of stress assumption, rather than the more usual displacement assumption.If the displacement assumption is used, an erroneous addition of the shear-deflection terms to the bending terms can be made if an apparently straightforward approach is utilized.

47 citations

Journal ArticleDOI
TL;DR: A hybrid method which uses the transfer matrix for the thin layer and the stiffness matrices for the thick layer is proposed and it is shown that the hybrid method has the same stability as the stiffness matrix method and the same round-off error as the transfer Matrix method.
Abstract: In this paper, a simple asymptotic method to compute wave propagation in a multilayered general anisotropic piezoelectric medium is discussed. The method is based on explicit second and higher order asymptotic representations of the transfer and stiffness matrices for a thin piezoelectric layer. Different orders of the asymptotic expansion are obtained using Pade approximation of the transfer matrix exponent. The total transfer and stiffness matrices for thick layers or multilayers are calculated with high precision by subdividing them into thin sublayers and combining recursively the thin layer transfer and stiffness matrices. The rate of convergence to the exact solution is the same for both transfer and stiffness matrices; however, it is shown that the growth rate of the round-off error with the number of recursive operations for the stiffness matrix is twice that for the transfer matrix; and the stiffness matrix method has better performance for a thick layer. To combine the advantages of both methods, a hybrid method which uses the transfer matrix for the thin layer and the stiffness matrix for the thick layer is proposed. It is shown that the hybrid method has the same stability as the stiffness matrix method and the same round-off error as the transfer matrix method. The method converges to the exact transfer/stiffness matrices essentially with the precision of the computer round-off error. To apply the method to a semispace substrate, the substrate was replaced by an artificial perfect matching layer. The computational results for such an equivalent system are identical with those for the actual system. In our computational experiments, we have found that the advantage of the asymptotic method is its simplicity and efficiency.

47 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented the complete force displacement relationship for a Timoshenko beam element resting on a two-parameter elastic foundation and derived the stiffness matrix and nodal-action column vector coefficients from the transport matrix based on the exact solution of two differential equations governing the problem concerned herein.
Abstract: The objective of this paper is to present the complete force-displacement relationship for a Timoshenko beam element resting on a two-parameter elastic foundation. Both the stiffness matrix and nodal-action column-vector coefficients are derived from the transport matrix based on the exact solution of two differential equations governing the problem concerned herein. Explicit expressions for the element stiffness matrix and the nodal-action column vectors are

47 citations


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