Analysis of continuum by the integrated force method

Patnaik, Surya N.; Nagaraj, M.

doi:10.1016/0045-7949(87)90106-4

Cited by 16 publications

(6 citation statements)

References 10 publications

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“…These conditions, when added to the Beltrami}Michell's Formulation, complete the method of stress in elasticity. CBMF solutions for plates and cylindrical shells are reported in References [4,18].…”

Section: Generation Of the Compatibility Conditions In Elasticitymentioning

confidence: 99%

“…In this paper, we discuss the bene"t gained from the use of the compatibility conditions in "nite element analysis. Similar bene"t in continuum analysis [18,20,21], design optimization, and structural testing is described in References [22}24]. To quantify the bene"t we have developed a research level "nite element code entitled &IFM/Analysers'.…”

Section: Benefit From the Compatibility Conditionsmentioning

confidence: 99%

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Compatibility conditions of structural mechanics

Patnaik

Coroneos

Hopkins

2000

Int. J. Numer. Meth. Engng.

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The theory of elasticity has camouflaged a glitch in the compatibility formulation since 1860. In structures the ad hoc compatibility conditions through virtual ‘cuts’ and closing ‘gaps’ is not parallel to the strain formulation in elasticity. The deficiency in the compatibility condition has prevented the development of direct stress determination method in structures and in elasticity. We have addressed and attempted to unify the theory of compatibility. This has lead to the development of the Integrated Force Method for structures and the Completed Beltrami–Michell's Formulation in elasticity. The utilization of the compatibility conditions allows mapping of variables and facile movement among different structural analysis formulations. This paper reviews and illustrates the requirement of compatibility in structures and in elasticity. Addresses the generation of the conditions and quantifies the benefit of their use. The traditional analysis methods and available solutions should be verified for compliance of the compatibility conditions. Published in 2000 by John Wiley & Sons, Ltd.

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Section: Generation Of the Compatibility Conditions In Elasticitymentioning

confidence: 99%

Section: Benefit From the Compatibility Conditionsmentioning

confidence: 99%

Compatibility conditions of structural mechanics

Patnaik

Coroneos

Hopkins

2000

Int. J. Numer. Meth. Engng.

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“…In elasticity, Patnaik et al . applied these principles in order to complete the Beltrami–Michell's formulation, and finally, he obtained the equations of IFM in continuous systems .…”

Section: Introductionmentioning

confidence: 99%

“…In 1986, he developed a variational functional for the IFM [4] based on the principles of virtual work and complementary virtual work. In elasticity, Patnaik et al applied these principles in order to complete the Beltrami-Michell's formulation, and finally, he obtained the equations of IFM in continuous systems [5,6].…”

Section: Introductionmentioning

confidence: 99%

The dual integrated force method applied to unidirectional composites

Adarraga

Cantera

Romera

et al. 2014

Numerical Meth Engineering

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SUMMARYThis paper shows the use of the dual integrated force method (IFMD) in finite elements method and its application to composite materials. This method was developed by S.N. Patnaik in isotropic materials, considering not only the equilibrium equations but also the compatibility conditions. In the IFMD, the principal unknowns are the displacements, and the structure of governing equation is similar to the stiffness method. It is shown that the governing equation of the IFMD is the same than in the case of the hybrid method of Pian. The method is applied to two examples, a cantilever beam of orthotropic material loaded at the end and one off-axis tensile test in a unidirectional composite specimen. The results of this method have been compared with the ones obtained from the application of the stiffness method and with analytical results.

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“…Research is in progress to alleviate the deficiency in the theory of solid mechanics. Benefits from the use of the completed strain formulation are being shown in continuum elasticity, [1][2][3][4][5][6] in finite element analysis, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and in design optimization. [26][27][28][29][30][31][32][33][34][35][36] The theory of strengths of materials began with the cantilever experiment conducted by Galileo in 1632.…”

Section: Introductionmentioning

confidence: 99%