• Structural Engineering and Mechanics
• /
• v.70 no.1
• /
• pp.125-131
• /
• 2019

A nine node isoparametric plate bending element is used for bending analysis of laminated composite skew cylindrical shell panels. Both thick and thin shell panels are solved. Rotary inertia and shear deformation are incorporated by considering first order shear deformation theory. The analysis is performed considering shallow shell theory. Both shallow and moderately deep skew cylindrical shells are investigated. Skew cylindrical shell panels having different thickness ratios (h/a), radius to length ratios (R/a), ply angle orientations, number of layers, aspect ratio (b/a), boundary conditions and various loading (concentrated, uniformly distributed, linear varying and doubly sinusoidal varying) conditions are analysed. Various new results are presented.

• Structural Engineering and Mechanics
• /
• v.18 no.1
• /
• pp.41-58
• /
• 2004

The postbuckling behaviour of thin shells has fascinated researchers because the theoretical prediction and their experimental verification are often different. In reality, shell panels possess small imperfections and these can cause large reduction in static buckling strength. This is more relevant in thin laminated composite shells. To study the postbuckling behaviour of thin, imperfect laminated composite shells using finite elements, explicit incremental or secant matrices have been presented in this paper. These incremental matrices which are derived using Marguerre's shallow shell theory can be used in combination with any thin plate/shell finite element (Classical Laminated Plate Theory - CLPT) and can be easily extended to the First Order Shear deformation Theory (FOST). The advantage of the present formulation is that it involves no numerical approximation in forming total potential energy of the shell during large deformations as opposed to earlier approximate formulations published in the literature. The initial imperfection in shells could be modeled by simply adjusting the ordinate of the shell forms. The present formulation is very easy to implement in any existing finite element codes. The secant matrices presented in this paper are shown to be very accurate in tracing the postbuckling behaviour of thin isotropic and laminated composite shells with general initial imperfections.

• Advances in aircraft and spacecraft science
• /
• v.3 no.3
• /
• pp.317-330
• /
• 2016

Nowadays, the interest of aerospace and automotive industries on virtual testing of medium-frequency vibrational behavior of shallow shell structures is growing. The development of software capable of predicting the vibrational response in such frequency range is still an open question because classical methods (i.e., FEM, SEA) are not fully suitable for the medium-frequency bandwidth. In this context the Variational Theory of Complex Rays (VTCR) is taking place as an ad-hoc technique to address medium-frequency problems. It is a Trefftz method based on a weak variational formulation. It allows great flexibility because any shape function that satisfies the governing equations can be used. This work further develops such theory. In particular, orthotropic materials are introduced in the VTCR formulation for shallow shell structures. A significant numerical example is proposed to show the strategy.

• Steel and Composite Structures
• /
• v.12 no.4
• /
• pp.303-324
• /
• 2012

This paper presents the mode-shape analysis of the cross-ply laminated composite cylindrical shallow shells. First, the kinematic relations of strains and deformation are given. Then, using Hamilton's principle, governing differential equations are developed for a general curved shell. Finally, the stress-strain relation for the laminated, cross-ply composite shells are obtained. By using some simplifications and assuming Fourier series as a displacement field, the governed differential equations are solved by the matrix algebra for shallow shells. Employing the computer algebra system called MATHEMATICA; a computer program has been prepared for the solution. The results obtained by this solution are compared with the results obtained by (ANSYS and SAP2000) programs, in order to verify the accuracy and reliability of the solution presented.

• Structural Engineering and Mechanics
• /
• v.81 no.2
• /
• pp.231-242
• /
• 2022

Numerical solutions for the linear buckling behavior of thin-walled circular hollow section members (CHS) with and without longitudinal stiffeners are presented using the semi-analytical finite strip method (SAFSM) which is developed based on Marguerre's shallow shell theory and Kirchhoff's assumption. The formulation of 3-nodal line finite strip is presented. The CHS members subjected to uniform axial compression, uniform bending, and combination of compression and bending. The buckling behavior of CHS is investigated through buckling curves which relate buckling stresses to lengths of the member. Effects of longitudinal stiffeners are studied with the change of its dimensions, position, and number.

• Structural Engineering and Mechanics
• /
• v.35 no.4
• /
• pp.493-510
• /
• 2010

This paper presents effects of anisotropy and curvature on free vibration characteristics of cross-ply laminated composite cylindrical shallow shells. Shallow shells have been considered for different lamination thickness, radius of curvature and elasticity ratio. First, kinematic relations of strains and deformation have been showed. Then, using Hamilton's principle, governing differential equations have been obtained for a general curved shell. In the next step, stress-strain relation for laminated, cross-ply composite shells has been given. By using some simplifications and assuming Fourier series as a displacement field, differential equations are solved by matrix algebra for shallow shells. The results obtained by this solution have been given tables and graphs. The comparisons made with the literature and finite element program (ANSYS).

• Steel and Composite Structures
• /
• v.33 no.2
• /
• pp.195-208
• /
• 2019

Based on a four-variable shear deformation shell theory, the free vibration analysis of functionally graded graphene platelet-reinforced composite (FGGPRC) doubly-curved shallow shells with different boundary conditions is investigated in this work. The doubly-curved shells are composed of multi nanocomposite layers that are reinforced with graphene platelets. The graphene platelets are uniformly distributed in each individual layer. While, the volume faction of the graphene is graded from layer to other in accordance with a novel distribution law. Based on the suggested distribution law, four types of FGGPRC doubly-curved shells are studied. The present shells are assumed to be rested on elastic foundations. The material properties of each layer are calculated using a micromechanical model. Four equations of motion are deduced utilizing Hamilton's principle and then converted to an eigenvalue problem employing an analytical method. The obtained results are checked by introducing some comparison examples. A detailed parametric investigation is performed to illustrate the influences of the distribution type of volume fraction, shell curvatures, elastic foundation stiffness and boundary conditions on the vibration of FGGPRC doubly-curved shells.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2008.03a
• /
• pp.1144-1154
• /
• 2008

In this paper, the behaviour of shell foundation was studied. In order to perform this study, three studies such as theoretical, numerical and experimental programs were performed. In the theoretical program, the general shallow foundation theories and failure mechanism developed by Terzaghi, Mayerhof and others were reviewed and compared. Based on the previous shallow foundation behaviour, the shell foundation theory was developed using the upper boundary theorem. In the numerical study, the 2 and 3 dimensional FEM simulations were carried out using an uncoupled-analysis approach. From the analysis results, the adequate depth of shell foundation was evaluated. It was also evaluated the bearing capacity according to the shell angle ($120^{\circ}$, $90^{\circ}$, $60^{\circ}$). In the experimental study, the laboratory model tests were carried out for five cases of different foundation shapes including the rectangular and circular foundation in order to verify the theoretical and nemerical study. According to the results of this study, the bearing capacity of shell foundation was theoretically about 15% larger than that of general foundation. However, in the model test, the bearing capacity of shell foundation was about 25 to 30% larger than that of general foundation. In the case of shell angle, the maximum bearing capacity of shell foundation shows when the shell angle of foundation was $60^{\circ}$. In addition, Even if the shell foundation has the various advantages compared with the general foundations as described above, the practical verifications in full scale size will be necessary to use in the field and will be helpful in the technical development of other special foundations.

• Steel and Composite Structures
• /
• v.51 no.4
• /
• pp.391-406
• /
• 2024

The present research investigates the combination resonance behaviors of porous FG shallow shells reinforced with oblique stiffeners and subjected to a two-term excitation. The oblique stiffeners considered in this research reinforce the shell internally and externally. To model the stiffeners, Lekhnitskii's smeared stiffeners technique is utilized. According to the first-order shear deformation theory (FSDT) and stress functions, a nonlinear model of the oblique stiffened shallow shell is established. With regard to the FSDT and von-Kármán nonlinear geometric assumptions, the stress-strain relationships for the present shell system are developed. Also, in order to discretize the nonlinear governing equations, the Galerkin method is implemented. To obtain the required relations for investigating the combination resonance theoretically, the method of multiple scales is applied. For verifying the results of the present research, generated results are compared with previous research. Additionally, a comparison with the P-T method is conducted to increase the validity of the generated results, as this method has illustrated advantages over other numerical methods in terms of accuracy and reliability. In this method, the piecewise constant argument is used jointly with the Taylor series expansion, which is why it is named the P-T method. The effects of stiffeners with different angles, and the effects of material parameters on the combination resonance behaviors of the present system are addressed. With the findings of this research, researchers and engineers in this field may use them as benchmarks for their design and research of porous FG shallow shells.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.04a
• /
• pp.283-290
• /
• 2001

Various laminates consisting of thin, unidirectional layers may be achieved by laying up laminae in different reinforcement directions and stacking sequences. Thus, the behavior of nonhomogeneous, anisotropic laminated structures is quite different from that of isotropic ones. The anisotropic laminated shell theory derived here, that includes the effect of transverse shear deformations, can give higher accuracy than thin shell theories. In this paper, by using closed-form solutions for shallow shells having simple supported boundary, extensive numerical study for anisotropic laminated shells were made to investigate the stacking sequence effects for various shells, and to show comparisons to the results between this paper and the existing literature.