Download e-book for iPad: A two-step perturbation method in nonlinear analysis of by Hui-Shen Shen

By Hui-Shen Shen

The strength to foretell the nonlinear reaction of beams, plates and shells whilst subjected to thermal and mechanical so much is of best curiosity to structural research. in reality, many buildings are subjected to excessive load degrees which could lead to nonlinear load-deflection relationships because of huge deformations. one of many very important difficulties deserving exact cognizance is the examine in their nonlinear reaction to massive deflection, postbuckling and nonlinear vibration.

A two-step perturbation procedure is to start with proposed by means of Shen and Zhang (1988) for postbuckling research of isotropic plates. This procedure provides parametrical analytical expressions of the variables within the postbuckling variety and has been generalized to different plate postbuckling occasions. This technique is then effectively utilized in fixing many nonlinear bending, postbuckling, and nonlinear vibration difficulties of composite laminated plates and shells, specifically for a few tough projects, for instance, shear deformable plates with 4 loose edges resting on elastic foundations, touch postbuckling of laminated plates and shells, nonlinear vibration of anisotropic cylindrical shells. This method can be stumbled on its extra broad purposes in nonlinear research of nano-scale structures. 

  • Concentrates on 3 different types of nonlinear analyses: vibration, bending and postbuckling
  • Presents not just the theoretical point of the innovations, but in addition engineering functions of the method

A Two-Step Perturbation technique in Nonlinear research of Beams, Plates and Shells is an unique and targeted procedure dedicated completely to unravel geometrically nonlinear difficulties of beams, plates and shells. it really is excellent for lecturers, researchers and postgraduates in mechanical engineering, civil engineering and aeronautical engineering.

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Additional info for A two-step perturbation method in nonlinear analysis of beams, plates and shells

Example text

1. 21 ðk1 ; k2 Þ ¼ ð0; 0Þ, P/Pcr ¼ 0 Present; Shen (2011) Yokoyama (1996) Timoshenko et al. 96 ð0:6p4 ; 0Þ for the Winkler model and (k1, k2) ¼ (0, 0) for a beam without any elastic foundation, as previously used by Yokoyama (1996). It can be seen that the results presented agree well with the exact solutions of Timoshenko et al. (1974) and Cheng and Pantelides (1988). In contrast, by using the finite element method, Yokoyama (1996) obtained higher values of v3 for each case. The results confirm that the compressive axial force reduces all modes of natural frequencies of the beams.

40 one has ! p p2 6  ð1Þ 3 m A10 l3 ¼ m 2 4 ð2:41Þ By solving the perturbation equation up to the fifth order, the asymptotic solutions can be obtained as 20 A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells    3  5 ð1Þ ð1Þ ð1Þ WðxÞ ¼ A10 e sin mx þ A10 e ½A330 sin 3mxŠ þ A10 e ½A530 sin 3mx þA550 sin 5mxŠ þ Oðe6 Þ    3 ð1Þ ð1Þ lq ¼ l1 A10 e þ l3 A10 e þ . . 43, the load–central deflection relationship can be written as    3 q0 L3 ð1Þ W m ð3Þ W m ¼ AW þ AW þÁÁÁ p4 EI L L ð2:45Þ in which, for case 1 (movable end condition) ð1Þ AW ð3Þ AW !

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