Investigation of strength and buckling of orthotropic conical shells and conical panels

E. O. Lapina ; A. A. Semenov

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 20 (2020) no. 1, pp. 79-92.

Résumé

In the construction, thin-walled shell structures are used to cover the buildings of large areas, such as stadiums, hangars, circuses, airports. In this paper, the strength and buckling of closed conical shells as well as their panels are studied. The geometric nonlinearity and transverse shifts are taken into account. A mathematical model is used in the form of a functional of the total potential energy of deformation. Also expressions for deformations, forces and moments are given. The calculation program is implemented in the MatLab environment. The algorithm is based on the Ritz method and Newton's method for solving a system of nonlinear algebraic equations. Variants of approximating functions for a closed shell and for its panel are shown. The values of critical loads are found, the dependence of the deflection on the load, the dependence of the stresses on the load is obtained, and the deflection field is shown at the subcritical and at the supercritical moment. The fields of various stress components are given at the moment when the strength conditions begin to fail. The orthotropy of the material is taken into account.

Bibliographie

[1] Hagihara S., Miyazaki N., “Bifurcation Buckling Analysis of Conical Roof Shell Subjected to Dynamic Internal Pressure by the Finite Element Method”, Journal of Pressure Vessel Technology, 125:1 (2003), 78–84 | DOI

[2] Krivoshapko S. N., “Research on General and Axisymmetric Ellipsoidal Shells Used as Domes, Pressure Vessels, and Tanks”, Applied Mechanics Reviews, 60:6 (2007), 336–355 | DOI

[3] Sosa E. M., Godoy L. A., “Challenges in the computation of lower-bound buckling loads for tanks under wind pressures”, Thin-Walled Structures, 48:12 (2010), 935–945 | DOI

[4] Gavryushin S. S., Nikolaeva A. S., “Method of change of the subspace of control parameters and its application to problems of synthesis of nonlinearly deformable axisymmetric thin-walled structures”, Mechanics of Solids, 51:3 (2016), 339–348 | DOI

[5] Solovei N. A., Krivenko O. P., Malygina O. A., “Finite element models for the analysis of nonlinear deformation of shells stepwise-variable thickness with holes, channels and cavities”, Magazine of Civil Engineering, 53:1 (2015), 56–69 | DOI

[6] Baranova D. A., Volynin A. L., Karpov V. V., “The Comparative Analysis of Calculation of Durability and Stability of the Supported Shells on the Basis of the PC OBOLOCHKA and PC ANSYS”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 10:4 (2010), 23–27 (in Russian) | DOI

[7] Karpov V. V., “Models of the shells having ribs, reinforcement plates and cutouts”, International Journal of Solids and Structures, 146 (2018), 117–135 | DOI

[8] Trach V. M., “Stability of conical shells made of composites with one plane of elastic symmetry”, International Applied Mechanics, 43:6 (2007), 662–669 | DOI

[9] Shadmehri F., Hoa S. V., Hojjati M., “Buckling of conical composite shells”, Composite Structures, 94:2 (2012), 787–792 | DOI

[10] Gupta A. K., Patel B. P., Nath Y., “Progressive damage of laminated cylindrical/conical panels under meridional compression”, European Journal of Mechanics – A/Solids, 53 (2015), 329–341 | DOI

[11] Dung D. V., Chan D. Q., “Analytical investigation on mechanical buckling of FGM truncated conical shells reinforced by orthogonal stiffeners based on FSDT”, Composite Structures, 159 (2017), 827–841 | DOI

[12] Dung D. V., Hoa L. Kh., Nga N. T., Anh L. T. N., “Instability of eccentrically stiffened functionally graded truncated conical shells under mechanical loads”, Composite Structures, 106 (2013), 104–113 | DOI

[13] Dai Q., Cao Q., “Parametric instability analysis of truncated conical shells using the Haar wavelet method”, Mechanical Systems and Signal Processing, 105 (2018), 200–213 | DOI

[14] Mehri M., Asadi H., Kouchakzadeh M. A., “Computationally efficient model for flow-induced instability of CNT reinforced functionally graded truncated conical curved panels subjected to axial compression”, Computer Methods in Applied Mechanics and Engineering, 318 (2017), 957–980 | DOI

[15] Najafov A. M., Mammadov Z., Kadioglu F., Zerin Z., Sofiyeve A. H., Tekin G., “Nonlinear Behavior of Composite Truncated Conical Shells Subjected to the Dynamic Loading”, Acta Physica Polonica A, 127:4 (2015), 904–906 | DOI

[16] Sofiyev A. H., Kuruoglu N., “Domains of dynamic instability of FGM conical shells under time dependent periodic loads”, Composite Structures, 136 (2016), 139–148 | DOI

[17] Sofiyev A. H., Pancar E. B., “The effect of heterogeneity on the parametric instability of axially excited orthotropic conical shells”, Thin-Walled Structures, 115 (2017), 240–246 | DOI

[18] Krysko V. A., Awrejcewicz J., Shchekaturova T. V., “Chaotic vibrations of spherical and conical axially symmetric shells”, Archive of Applied Mechanics, 74:5–6 (2005), 338–358 | DOI

[19] Patel B. P., Khan K., Nath Y., “A new constitutive model for bimodular laminated structures: Application to free vibrations of conical/cylindrical panels”, Composite Structures, 110 (2014), 183–191 | DOI

[20] Qu Y., Chen Y., Long X., Hua H., Meng G., “A modified variational approach for vibration analysis of ring-stiffened conical-cylindrical shell combinations”, European Journal of Mechanics – A/Solids, 37 (2013), 200–215 | DOI

[21] Shul'ga N. A., Bogdanov S. Yu., “Forced Axisymmetric Nonlinear Vibrations of Reinforced Conical Shells”, International Applied Mechanics, 39:12 (2003), 1447–1451 | DOI

[22] Demir Ç., Mercan K., Civalek Ö., “Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel”, Composites Part B : Engineering, 94 (2016), 1–10 | DOI

[23] Khan A. H., Patel B. P., “On the nonlinear dynamics of bimodular laminated composite conical panels”, Nonlinear Dynamics, 79:2 (2015), 1495–1509 | DOI

[24] Zerin Z., “The effect of non-homogeneity on the stability of laminated orthotropic conical shells subjected to hydrostatic pressure”, Structural Engineering and Mechanics, 43:1 (2012), 89–103 | DOI

[25] Hao Y. X., Yang S. W., Zhang W., Yao M. H., Wang A. W., “Flutter of high-dimension nonlinear system for a FGM truncated conical shell”, Mechanics of Advanced Materials and Structures, 25:1 (2018), 47–61 | DOI

[26] Maksimyuk V. A., Storozhuk E. A., Chernyshenko I. S., “Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)”, International Applied Mechanics, 48:6 (2012), 613–687 | DOI

[27] Sankar A., Natarajan S., Merzouki T., Ganapathi M., “Nonlinear Dynamic Thermal Buckling of Sandwich Spherical and Conical Shells with CNT Reinforced Facesheets”, International Journal of Structural Stability and Dynamics, 2016, 1750100 | DOI

[28] Watts G., Singha M. K., Pradyumna S., “Nonlinear bending and snap-through instability analyses of conical shell panels using element free Galerkin method”, Thin-Walled Structures, 122 (2018), 452–462 | DOI

[29] Semenov A. A., “Strength and stability of geometrically nonlinear orthotropic shell structures”, Thin-Walled Structures, 106 (2016), 428–436 | DOI

[30] Semenov A. A., “Analysis of the strength of shell structures, made from modern materials, according to various strength criteria”, Diagnostics, Resource and Mechanics of Materials and Structures, 2018, no. 1, 16–33 | DOI

[31] Smerdov A. A., Buyanov I. A., Chudnov I. V., “Analysis of optimal combinations of requirements to developed CFRP for large space-rocket designs”, Proceedings of Higher Educational Institutions. Machine Building, 2012, no. 8, 70–77 (in Russian) | DOI

[32] Tsepennikov M. V., Povyshev I. A., Smetannikov O. Yu., “Verification of numerical technique for composite structures failure modeling”, Perm National Research Polytechnic University Bulletin. Applied Mathematics and Mechanics, 2012, no. 10, 225–241 (in Russian)