A two-step perturbation method in nonlinear analysis of by Hui-Shen Shen

By Hui-Shen Shen

The potential 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 that could lead to nonlinear load-deflection relationships as a result of huge deformations. one of many very important difficulties deserving targeted recognition is the learn in their nonlinear reaction to giant deflection, postbuckling and nonlinear vibration.

A two-step perturbation approach is to start with proposed via Shen and Zhang (1988) for postbuckling research of isotropic plates. This technique supplies parametrical analytical expressions of the variables within the postbuckling variety and has been generalized to different plate postbuckling events. This strategy is then effectively utilized in fixing many nonlinear bending, postbuckling, and nonlinear vibration difficulties of composite laminated plates and shells, particularly for a few tough initiatives, for instance, shear deformable plates with 4 unfastened edges resting on elastic foundations, touch postbuckling of laminated plates and shells, nonlinear vibration of anisotropic cylindrical shells. This process can be stumbled on its extra wide functions in nonlinear research of nano-scale structures. 

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

A Two-Step Perturbation strategy in Nonlinear research of Beams, Plates and Shells is an unique and specified procedure committed solely to unravel geometrically nonlinear difficulties of beams, plates and shells. it truly 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

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The displacement components are assumed to have the form U 1 ¼ UðX; Y; tÞ þ ZCx ðX; Y; tÞ þ Z 2 jx ðX; Y; tÞ þ Z 3 zx ðX; Y; tÞ ð3:1aÞ U 2 ¼ VðX; Y; tÞ þ ZCy ðX; Y; tÞ þ Z 2 jy ðX; Y; tÞ þ Z 3 zy ðX; Y; tÞ ð3:1bÞ U 3 ¼ WðX; Y; tÞ ð3:1cÞ where t represents time, U, V, W, Cx , Cy , jx , jy , zx and zy are unknowns. If the transverse shear stresses s 4 and s 5 are to vanish at the bounding planes of the plate (at Z¼Æh/2), the transverse shear strains e4 and e5 should also vanish there. 1 leads to the following displacement field "   # 4 Z 2 @W U 1 ¼ U þ Z Cx À x Cx þ ; 3 h @X   # 4 Z 2 @W ; Cy þ U 2 ¼ V þ Z Cy À x 3 h @Y ð3:5aÞ " U 3 ¼ W; ð3:5bÞ ð3:5cÞ in which x is a tracer.

Computational Materials Science 50: 1022–1029. Shen H-S, Zhang JW. (1988). Perturbation analyses for the postbuckling of simply supported rectangular plates under uniaxial compression. Applied Mathematics and Mechanics 9: 793–804. Timoshenko SP, Gere JM. (1961). Theory of Elastic Stability. McGraw-Hill, New York. Timoshenko SP, Young DH, Weaver W. (1974). Vibration Problems in Engineering. , New York. Toakley AR. (1965). Buckling loads for elastically supported struts. Journal of Engineering Mechanics Division ASCE 91: 205–231.

The full nonlinear terms in addition to the usual von Karman nonlinearities were included. These nonlinearities were found to affect the nonlinear frequencies of moderate thick plates by as much as 30–63%. For some geometric parameters, the nonlinear effects were greater for A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells, First Edition. Hui-Shen Shen. Ó 2013 by Higher Education Press. All rights reserved. Published 2013 by John Wiley & Sons Singapore Pte. Ltd.

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