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 leading curiosity to structural research. actually, many constructions are subjected to excessive load degrees which may bring about nonlinear load-deflection relationships because of huge deformations. one of many vital difficulties deserving distinctive consciousness is the examine in their nonlinear reaction to giant deflection, postbuckling and nonlinear vibration.

A two-step perturbation procedure is to begin with proposed via Shen and Zhang (1988) for postbuckling research of isotropic plates. This procedure supplies parametrical analytical expressions of the variables within the postbuckling diversity and has been generalized to different plate postbuckling occasions. This strategy 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 initiatives, 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 came across 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 element of the recommendations, but additionally engineering functions of the method

A Two-Step Perturbation procedure in Nonlinear research of Beams, Plates and Shells is an unique and targeted approach dedicated totally 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 resources for A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells (Information Security)

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Journal of Applied Physics 104: 033543. Yokoyama T. (1996). Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations. Computers and Structures 61: 995–1007. Zhao MH, He W, Li QS. (2010). Post-buckling analysis of piles by perturbation method. Structural Engineering and Mechanics 35: 191–203. Zhou C-T. (1981). Theory of Elastic Stability (in Chinese) Sichuan People’s Publishing House, Chengdu. 1 Introduction In this chapter attention is paid to the prediction of the nonlinear vibration characteristics of composite plates by using a two-step perturbation method.

2001), Patel et al. (2002) and Shen et al. (2004). Gandhi et al. (1988) studied the nonlinear vibration of laminated composite plates in hygrothermal environments. In their analysis the formulations were based on the first-order shear deformation plate theory (FSDPT) and the numerical results were only for the free vibration of a cantilevered laminated composite beam. Huang et al. (2004) studied the nonlinear vibration and dynamic response of shear deformable laminated plates in hygrothermal environments based on a higher order shear deformation plate theory (HSDPT).

5 are e1 ¼ e01 þ Zðk01 þ Z 2 k21 Þ; e2 ¼ e02 þ Zðk02 þ Z 2 k22 Þ; e3 ¼ 0; e4 ¼ e04 þ Z 2 k24 ; e5 ¼ e05 þ Z 2 k25 ; e6 ¼ e06 þ Zðk06 þ Z 2 k26 Þ; ð3:6Þ 32 A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells where    2 @U 1 @W @Cx 2 4 @Cx @ 2 W 0 ; k1 ¼ Àx 2 þ ; þ ¼ ; k1 ¼ @X @X @X 2 @X @X 2 3h    2 @V 1 @W @Cy 2 4 @Cy @ 2 W 0 0 e2 ¼ ; ; k2 ¼ Àx 2 þ ; k2 ¼ þ @Y @Y @Y 2 @Y @Y 2 3h   @W 2 4 @W e04 ¼ Cy þ ; k4 ¼ Àx 2 Cy þ ; @Y @Y h   @W 2 4 @W 0 ; k5 ¼ Àx 2 Cx þ ; e5 ¼ C x þ @X @X h   @U @V @W @W 0 @Cx @Cy 2 4 @Cx @Cy @2W 0 þ ; k6 ¼ Àx 2 þ þ2 þ þ ; k6 ¼ ; e6 ¼ @Y @X @Y @X @Y @X @X @Y @X@Y 3h ð3:7Þ The plane stress constitutive equations may then be written in the form e01 2 s1 3 2 Q11 Q12 6 7 6 4 s 2 5 ¼ 4 Q21 s6 s4 # s5 ¼ e1 3 Q44 0 0 Q55 #" e4 # ; e5 As in the classical plate theory, the stress resultants and couples are defined by ð h=2 s i ð1; Z; Z 3 Þ dZ; ði ¼ 1; 2; 6Þ ðN i ; M i ; Pi Þ ¼ Àh=2 ðQ2 ; R2 Þ ¼ ð h=2 Àh=2 ðQ1 ; R1 Þ ¼ ðh Àh ð3:8aÞ e6 Q66 0 " 32 76 7 0 54 e2 5; Q22 0 " 0 s 4 ð1; Z 2 ÞdZ; s 5 ð1; Z 2 ÞdZ; ð3:8bÞ ð3:9aÞ ð3:9bÞ ð3:9cÞ where N i and Qi are membrane and transverse shear forces, M i is bending moment per unit length and Pi and Ri are higher order bending moment and shear force, respectively.

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