Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T16:49:45.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Mixed-Form Equations for Stiffened Orthotropic Shells of Arbitrary Canonical Shape with Static Loading

Published online by Cambridge University Press:  02 October 2017

V. V. Karpov  and
A. A. Semenov
V. V. Karpov*
Affiliation:
Department of Applied Mathematics and InformaticsSaint-Petersburg State University of Architecture and Civil EngineeringSaint-Petersburg, Russia
A. A. Semenov
Affiliation:
Department of Applied Mathematics and InformaticsSaint-Petersburg State University of Architecture and Civil EngineeringSaint-Petersburg, Russia
*
*Corresponding author (vvkarpov@lan.spbgasu.ru)
Get access

Abstract

Thin-walled orthotropic shells of arbitrary form reinforced from the concave side by a cross-sectional stiffening system oriented in parallel to coordinate lines are examined. Geometrical nonlinearity and transverse shears are taken into account, but it is presumed that a shell is shallow.

Mixed-form equations are more simplified equations of a shell theory as compared to displacement equations, but they are more convenient for some types of fixing of the shell edges (for example, for movable pin fixing).

Forces are expressed using a stress function in a middle surface of a shell in such a way that the first two equilibrium equations are satisfied identically. Shell deformation is also expressed using this function.

The third equation of strain compatibility is used to form one of the mixed-form equations. Curvature and torsion change functions for this equation are written in the same way as for the Kirchhoff–Love model, though also taking into account transverse shears.

Keywords

Stiffened shellsMathematical modelOrthotropyMixed-form equations
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 469 - 474
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Vlasov, V. Z., “The General Theory of Shells and Its Application in Engineering,” Gostehizdat, Moscow, Leningrad, Russia (1949). (in Russian)Google Scholar
2. Petrov, V. V., “Analysis of Flexible Plates and Shallow Shells by the Method of V. Z. Vlasov,” Soviet Applied Mechanics, 2, pp. 32–36 (1966).Google Scholar
3. Krysko, V. A., Awrejcewicz, J. and Komarov, S. A., “Nonlinear Deformations of Spherical Panels Subjected to Transversal Load Action,” Computer Methods in Applied Mechanics and Engineering, 194, pp. 3108–3126 (2005).Google Scholar
4. Librescu, L., “Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures,” Noordhoff International Publishing, Leyden, Netherlands (1975).Google Scholar
5. Librescu, L. and Chang, M.-Y., “Imperfection Sensitivity and Postbuckling Behavior of Shear-Deformable Composite Doubly-Curved Shallow Panels,” International Journal of Solids and Structures, 29, pp. 1065–1083 (1992).Google Scholar
6. Feng, W.-Z., Chen, Z.-P., Jiao, P., Zhou, F. and Fan, H.-G., “Buckling of Cylindrical Shells with Arbitrary Circumferential Thickness Variations under External Pressure,” Journal of Mechanics, 33, pp. 55–65 (2017).Google Scholar
7. Bich, D. H., Nam, V. H. and Phuong, N. T., “Nonlinear Postbuckling of Eccentrically Stiffened Functionally Graded Plates and Shallow Shells,” Vietnam Journal of Mechanics, 33, pp. 131–147 (2011).Google Scholar
8. Dung, D. V. and Dong, D. T., “Post-Buckling Analysis of Functionally Graded Doubly Curved Shallow Shells Reinforced by FGM Stiffeners with Temperature-Dependent Material and Stiffener Properties Based on TSDT,” Mechanics Research Communications, 78, pp. 28–41 (2016).Google Scholar
9. Spasskaya, M. V. and Treshchev, A. A., “Thermoelastic Deformation of the Cylindrical Shell Made of Anisotropic Different Resistant Material,” Bulletin of the Yakovlev Chuvash State Pedagogical University, Series: Mechanics of Limit State, 1, pp. 65–74 (2015). (in Russian)Google Scholar
10. Shen, S.-H. and Yang, D.-Q., “Nonlinear Vibration of Anisotropic Laminated Cylindrical Shells with Piezoelectric Fiber Reinforced Composite Actuators,” Ocean Engineering, 80, pp. 36–49 (2014).Google Scholar
11. Zhang, J. and van Campen, D. H., “Stability and Bifurcation of Doubly Curved Shallow Panels under Quasi-Static Uniform Load,” International Journal of Non-Linear Mechanics, 38, pp. 457–466 (2003).Google Scholar
12. van Campen, D. H., Bouwman, V. P., Zhang, G. Q. and ter Weeme, B. J. W., “Semi-Analytical Stability Analysis of Doubly-Curved Orthotropic Shallow Panels – Considering the Effects of Boundary Conditions,” International Journal of Non-Linear Mechanics, 37, pp. 659–667 (2002).Google Scholar
13. Seffen, K. A., “Morphing Bistable Orthotropic Elliptical Shallow Shells,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463, pp. 67–83 (2007).Google Scholar
14. Karpov, V. V. and Semenov, A. A., “Mathematical Models and Algorithms for Studying Strength and Stability of Shell Structures,” Journal of Applied and Industrial Mathematics, 11, pp. 70–81 (2017).Google Scholar
15. Sukhinin, S. N., Applied Problems of Stability of Multilayered Composite Shells, Fizmatlit, Moscow (2010). (in Russian)Google Scholar
16. Novozhilov, V. V., The Theory of Thin Shells, Sudpromizdat, Leningrad, Russia (1962). (in Russian)Google Scholar
17. Reissner, E., “On Asymptotic Solutions for Nonsymmetric Deformations of Shallow Shells of Revolution,” International Journal of Engineering Science, 2, pp. 27–43 (1964).Google Scholar
18. Gol'denveyzer, A. L., “The Equations of the Theory of Shells,” PMM, 2 (1940). (in Russian)Google Scholar