In this paper, 2D boundary element stress analysis is carried out to obtain the T-stress for multiple internal edge cracks in thick-walled cylinders for a wide range of cylinder radius ratios and relative crack depth. The T-stress, together with the stress intensity factor K, provides a more reliable two-parameter prediction of fracture in linear elastic fracture mechanics. T-stress weight functions are then derived from the T-stress solutions for two reference load conditions corresponding to the cases when the cracked cylinder is subject to a uniform and to a linear applied stress variation on the crack faces. The derived weight functions are then verified for several non-linear load conditions. Using the BEM results as reference T-stress solutions; the T-stress weight functions for thick-walled cylinder have also been derived. Excellent agreements between the BEM results and weight function predictions are obtained. The weight functions derived are suitable for obtaining Tstress solutions for the corresponding cracked thick-walled cylinder under any complex stress fields. Results of the study show that the two dimensional BEM analysis, together with weight function method, can be used to provide a quick and accurate estimate of T-stress for 2-D crack problems.

Shell structures have various applications in Civil and Mechanical engineering. Shells, like other types of structure, are subject to damage and deterioration, such as development and propagation of cracks. In this research, the effect of a full penetration non - propagating macro crack, with various parameters, on natural vibration frequencies and mode shapes, is investigated. For this purpose, 400 cracked shell models have been created. These shells are grouped into cylindrical panels and full cylindrical shells and the effect of various parameters, such as crack length, crack orientation, thickness, poison ratio, shell height and panel's central angle, on the vibration frequencies and mode shapes of the shells, has been investigated.

The plastic behavior of an elastoplastic cylindrical shell with circular and rectangular cutouts underbending moment loads was investigated numerically and experimentally. A testing device (pure bending measurement) was designed and made to perform experiments on bending moment tests. The ratio of diameter to thickness of the stainless steel 304 specimens was 40.4 and the ratio of length to diameter was 7.94. The shape of the cutout on the shell was circular or rectangular. The tested specimens were categorized into five dissimilar groups. The effect of size, position and numbers of the cutout on the plastic moment is discussed. In order to investigate the strain distribution around of cutout, nine strain gauges were mounted in the longitudinal and circumferential directions on two specimens with different type of cutout. To investigate the accuracy of analytical and experimental results, numerical analysis considering the behavior of elastoplastic material was performed and good agreement was obtained between them. The strength of bending moment of cylindrical shells was decreased with increasing of sizes of cutout and it was increased with changing the location of the cutout from compression side to tension side. The effect of the number of cutouts (increasing from 1 to 3 (axisymmetrical) on bending strength of tubes is negligible.      

Thin-walled cylindrical shells are extensively used in civil engineering. Due to thin wall thickness, they are vulnerable to stability failure in the form of shell buckling. The European Standard in design of steel structures is considered to be a pioneer in strength and stability assessment of shell structures. Wind pressure and seismic action lead to non-uniform distributed transverse loading on cylindrical shells. It has been shown that non-uniform loading may have a significant and deleterious effect on the structural stability of these structures. The present study deals with buckling behavior of short cylindrical shells under three non-uniform distributed transverse pressures. The loading patterns were adopted in a way to simulate the normal pressures due to ensiled materials in excited situation. It was done with respect to Eurocode design provisions for earthquake resistance of circular silos. Its aim is to produce useful information for the design of cylindrical shells against buckling under general transverse loading. An overview of Eurocode treatments of shell stability using finite element analysis is presented. In addition, the paper explores the effects of different forms of transverse loading on stability response of the structure. The numerical approach was selected to fulfill the stability evaluations. Eurocode has many provisions for the global analysis of shell structures using finite element analysis. Hence, a full suite of computational shell buckling calculations was performed according to this standard. Linear bifurcation analysis was undertaken, firstly. It served as a benchmark for further evaluations. Two different linear bifurcation eigenmodes were observed. The main mode of buckling was diagonal shear wrinkles near the base of silo with partial extension in circumferential direction. The other mode was local axial compression buckle at the foot of the shell. A wide range of imperfection sensitivity studies using these eigenmodes were conducted. The imperfections can take many forms and can have different amplitudes. Some imperfection forms may result in higher strength of the shell. This makes identifying the worst condition very challenging. A sample parametric study on imperfection amplitude in forms of eigenmodes, illustrated this kind of analysis. Additionally, the effect of plasticity was explored through the ideal elastic-plastic model for steel. It was shown that due to loading pattern, the plasticity may cause different amount of reduction in elastic load factor. To establish the actual plastic collapse load, the modified Southwell plots were used. To achieve more realistic evaluation of buckling and post-buckling behavior of thin-walled cylinders, the finite element analyses should include all possible source of strength reduction in stability of the shell structures. To this end the geometrically and materially non-linear analysis with explicit inclusion of imperfections (GMNIA) is considered to be the most advanced form of numerical analysis. The load factors derived from GMNIA analyses showed a stability reduction more than half as compared to linear bifurcation analyses in two load cases. The non-linear incremental buckling modes were also explored. Finally, the general shape of buckled short cylinders under transverse loading was characterized by combination of diagonal shear wrinkles and elephant’ s foot buckling mode.

Fiber-reinforced composite materials continue to experience increased adoption in aerospace, marine, automobile, and civil structures due to their high specific strength, high stiffness, and light weight. This increased use has been accompanied by applications involving non-traditional configurations such as compression members with elliptical cross-sections. To model such shapes, we develop and report an improved generalized shell element called 4EAS-FS through a combination of enhanced assumed strain and the substitute shear strain fields. A flat shell element has been developed by combining a membrane element with drilling degree-of-freedom and a plate bending element. We use the element developed to determine specifically buckling loads and mode shapes of composite laminates with elliptical cross-section including transverse shear deformations. The combined influence of shell geometry and elliptical cross-sectional parameters, fiber angle, and lay-up on the buckling loads of an elliptical cylinder is examined. It is hoped that the critical buckling loads and mode shapes presented here will serve as a benchmark for future investigations.

In this study, the free vibration of partially fluid-filled laminated composite circular cylindrical shell with arbitrary boundary conditions has been investigated by using Rayleigh-Ritz method. The analysis has been carried out with strain-displacement relations based on Love’s thin shell theory and the contained fluid is assumed irrotational, incompressible and inviscid. After determining the kinetic and potential energies of fluid filled laminated composite shell, the eigenvalue problem has been obtained by means of Rayleigh-Ritz method. To demonstrate the validity and accuracy of the results, comparison has been made with the results of similar works for the empty and partially fluid-filled shells. Finally, an extensive parameter study on a typical composite tank is accomplished and some conclusions are drawn.

In this paper, a unified analytical approach is proposed to investigate vibrational behavior of functionally graded shells. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stoke's transformation. Material properties are assumed to be graded in the thickness direction according to different volume fraction functions such as power-law, sigmoid, double-layered and exponential distributions. A FGM cylinderical shell made up of a mixture of ceramic and metal is considered. The Influence of some commonly used boundary conditions, the effect of changes in shell geometrical parameters and variations of volume fraction functions on the vibration characteristics are studied by comparing the results from the present theory with those from the First order Shear Deformation Theory (FSDT). Furthermore, the results obtained for a number of particular cases show good agreement with those available in the open literature. The simplicity and the capability of the present method are also discussed.