On the theory of discrete structural model analysis and design

Panditta, Inder Krishen; Shimpi, Rameshchandra P.; Prasad, K. Satya

doi:10.1016/s0020-7683(98)00066-3

Cited by 4 publications

(8 citation statements)

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“…[15,16]. According to this principle quasi work, 'W mn ', done by external forces of one system (say 'm') while go ing through the corresponding displacements of the other topologically similar system (say 'n') is equal to the quasi strain energy, 'U mn ', due to internal forces of former system ('m') wh ile going through corresponding deformat ions of the latter system ('n').…”

Section: Principle Of Quasi Workmentioning

confidence: 99%

“…(15) necessitates that the radius of two shafts should be equal. Hence, for shafts to be topologically similar their d iameter should be equal.…”

Section: Topological Similar Shaftsmentioning

confidence: 99%

“…PQW thus fills existing void in the domain of structural mechanics. Using PQW, so me useful theorems for discrete structural models were derived by [5,15]. PQW was adv ant ag eous ly used by [16] fo r ob tain ing redund ant react ions o f beams .…”

Section: Introductionmentioning

confidence: 99%

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Deflection of Structures using Principle of Quasi Work

Panditta¹,

Wani²

2013

AEROSPACE

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A new methodology for obtaining deflections of structures is presented in this paper. It is based on Principle of Quasi Work, which connects two topologically similar systems thereby leading to a unique concept of standard elements for every category of structural problems. Using a priory known equation of deformation/deflection of elastic axis of these elements, solution for equation of deformed/ deflected elastic line of other structural members of similar category having different loading and boundary conditions is presented here. Th is methodology is easy to use as deflection of a given structure is obtained mostly by simple mu ltiplications and it also eliminates the use of internal force/bending mo ment expressions unlike conventional methods. Even though this methodology can be applied to any structure, its use is illustrated for one dimensional structural elements (viz. axial bars, torsion rods and beams) for the sake of conciseness and clarity. The concept of topologically similar system is exp lored for each category of elements as it lies at the heart of the principle of quasi work.

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Section: Principle Of Quasi Workmentioning

confidence: 99%

“…(15) necessitates that the radius of two shafts should be equal. Hence, for shafts to be topologically similar their d iameter should be equal.…”

Section: Topological Similar Shaftsmentioning

confidence: 99%

See 1 more Smart Citation

Deflection of Structures using Principle of Quasi Work

Panditta¹,

Wani²

2013

AEROSPACE

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“…In the statement of PQW, topology for discrete structural models (as given by Panditta [6] and Panditta et al [14]) specifies a unique set of nodes and their interconnectivity in a system. For TSS, the physical/ material properties and the constitutive relations of branch elements (connecting different nodes) are immaterial.…”

Section: Principal Of Quasi Workmentioning

confidence: 99%

“…The existing energy methods [8,9], variational principles [10,11], and finite element methods [12,13] are meant for a single system and do not provide any connection to two structural systems. Panditta et al [14] derived theorems useful for discrete structural models characterizing stiffness, mass, and damping properties of structural elements forming the lower end of finite elements by using this powerful quasi energy theorem. Munshi and Tikoo [15] developed a demonstrative interactive computer graphic program for obtaining redundant reaction of single degree indeterminate beams.…”

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confidence: 99%

Redundant Reactions of Indeterminate Beams by Principle of Quasi Work

2010

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A new methodology for determining redundant reactions of beams is presented in this paper. This methodology is based on the principle of quasi work, which is a powerful pseudoenergy theorem deduced from Tellegen's theorem. It takes topography of a structural system as a variable in addition to the variables involved in conventional energy methods, variational principles, and finite element methods. The concept of topologically similar system lies at the heart of the principle of quasi work. This concept is explored for beams to define topologically similar beams and topologically equivalent beams. The principle of quasi work is validated for beams and subsequently used for determining redundant reactions of indeterminate and continuous beams. Further, a unique concept of reference beam is developed. Equation of deflection curve of this reference beam is used to solve redundant reactions of indeterminate beams. This methodology has an advantage of calculating redundant reactions mostly by simple multiplications without any integrations or differentiations and does not require any prior knowledge of writing bending moment expressions. The method is illustrated through examples. It is possible to develop an interactive graphic computer package for calculating reactions of indeterminate beams. Nomenclature A n = cross-section area of beam represented by TSS n fdg n = displacement in TSS n corresponding to fPg m E n = Young's modulus of elasticity of beam represented by TSS n fFg m = internal forces in a TSS m L n = length of beam represented by TSS n M n = bending moment in the beam represented by TSS n M n = mapped bending moment in the beam represented by TSS n M = moment reaction on beam from support , in which represents A, B, C, etc. fPg m = external loads acting on TSS m R= reaction on beam from support , in which represents A, B, C, and 0, 1, 2, etc. U mn = quasi energy fFg T m fg n W mn = quasi energy fPg T m fdg n vx = beam deflection as a function of x w = intensity of uniformly distributed load x n = coordinate along longitudinal axis of beam represented by TSS n y = coordinate along the depth of beam measured from neutral axis fg n = deformation in TSS n corresponding to fFg m "x = strain as a function of x in the beam x = stress as a function of x in the beam = nondimensional parameter x n =L n m, n = subscripts 1,2,3, etc., representing different topologically similar systems hexp :i = if exp : 0 the value of the bracket 0;otherwise, it is equal to exp : fexp :g n = exp : is for TSS n

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