# The theorems of structural variation for rectangular finite elements for plate flexure

2005-11-01
Saka, MP
The theorems of structural variation predict the forces and displacements throughout a structure without the need of fresh analysis when the physical properties of one or more members are altered or even its topology is changed due to removal of one or more of its elements. It has been shown that a single linear elastic analysis of a parent structure under the applied loads and a set of unit-loading cases is sufficient to determine the elastic, non-linear elastic and even elasticplastic response of number of related frames. These theorems later are extended to triangular, quadrilateral and solid cubic finite element structures. In this paper, the theorems of structural variation are extended to cover the rectangular finite elements for plate flexure. The unit-loading cases required to study the modification of a single element are derived. The displacements and nodal forces obtained from these unit-loading cases are used to calculate the variation factors. Multiplication of the response of the parent structure by these variation factors simply yields the response of the new structures where one or more of its members are altered or totally removed. Two examples are included to demonstrate the application of these theorems.
COMPUTERS & STRUCTURES

# Suggestions

 EXTENSION OF THE RESIDUAL VARIABLE METHOD TO PROPAGATION PROBLEMS AND ITS APPLICATION TO THE WAVE-EQUATION IN CYLINDRICAL COORDINATES AKKAS, N; Tokdemir, Turgut (Elsevier BV, 1992-08-03) Consider a partial differential equation with cylindrical coordinates describing a dynamic process in an infinite medium with an inner cylindrical boundary. If an analytical solution to the problem is not possible, then one resorts to numerical techniques. In this case it becomes necessary to discretize the infinite domain even if the solution is required on the inner cylindrical surface or at a limited number of points in the domain only. The residual variable method (RVM) circumvents the difficulty associ...
 MODELING OF CONTROL FORCES FOR KINEMATICAL CONSTRAINTS IN MULTIBODY SYSTEMS DYNAMICS - A NEW APPROACH IDER, SK (Elsevier BV, 1991-01-01) Conventionally kinematical constrains in multibody systems are treated similar to geometrical constraints and are modeled by constraint reaction forces which are perpendicular to constraint surfaces. However, in reality, one may want to achieve the desired kinematical conditions by control forces having different directions in relation to the constraint surfaces. In this paper the conventional equations of motion for multibody systems, subject to kinematical constraints, are generalized by introducing gener...
 A SHEAR FLEXIBLE FINITE-ELEMENT FOR NONUNIFORM, LAMINATED COMPOSITE BEAMS Oral, Süha (Elsevier BV, 1991-01-01) A shear flexible finite element is formulated for linearly tapered, symmetrically laminated composite beams. The element has three nodes and 18 degrees of freedom. The three-node configuration is obtained from a five-node parent element by constraining the shear angle variation to be linear. The bending in two planes, twisting and stretching are considered. The performance of the element is tested with isotropic and composite materials, constant and variable cross-sections, and straight and curved geome...
 ISOPARAMETRIC ELEMENTS WITH UNEQUALLY SPACED EDGE NODES UTKU, M; CITIPITIOGLU, E; OZKAN, G (Elsevier BV, 1991-01-01) In the isoparametric finite element formulation, mapping of equally spaced nodes on the boundary of the master element to unequally spaced locations on the physical elements results in an unacceptable distortion. This type of distortion is defined as 'node mapping distortion' and a technique for its elimination is presented. Simple test cases demonstrate the utility of the new formulation.
 An investigation of accuracy of inertial interaction analyses with frequency-independent impedance coefficients Yılmazok, Özgün; Bakır, Bahadır Sadık; Department of Civil Engineering (2007) The inertial interaction between the soil and structure alters dynamic response characteristics of a structure due to foundation deformability, such that the flexibility and energy dissipation capability of surrounding soil may lead to a significant increase in period and damping of structural oscillations. The inertial interaction analyses can be accomplished through utilisation of frequency dependent foundation impedance coefficients that are reported in literature for various soil conditions and foundati...
Citation Formats
M. Saka, “The theorems of structural variation for rectangular finite elements for plate flexure,” COMPUTERS & STRUCTURES, pp. 2442–2452, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63549.