J.N. Bandyopadhyay

Free vibration analysis of point-supported laminated composite doubly curved shells—A finite element approach

Abstract A finite element analysis for studying the free vibration behaviour of generalized doubly curved laminated composite shells is presented using eight-noded curved quadrilateral isoparametric finite elements. The formulation assumes first-order shear deformation theory for thin and shallow shells, and also considers the two principal radii of curvature and the radius of cross-curvature. Some of the results obtained are compared with those present in the existing literature. Several other numerical results are presented by varying fibre orientations, lamination schemes, support spacings, aspect ratio, lower height to higher height ratio (for conoids), the thickness to radius ratio and radii of curvature ratio (for elliptic and hyperbolic paraboloids), which are relevant to the doubly curved shells.

Nonlinear Free Vibration Analysis of Laminated Composite Cylindrical Shells with Cutouts

The nonlinear free vibration of laminated composite cylindrical shell panels in the presence of cutouts is investigated. The finite element model using an eight-noded C0 continuity, isoparametric quadrilateral element is used to study the dynamic behavior. The nonlinear eigenvalue problem is solved by using the direct iteration method. Parametric study is carried out varying the aspect ratios, lamination schemes and material properties of cylindrical shell with simply supported boundary condition in the presence of cutouts.

Bending analysis of conoidal shells using curved quadratic isoparametric element

Doubly curved conoidal shells are being increasingly used for many industrial and similar structures. They are aesthetically pleasing, and are easy to construct because of their ruled surface. The variation of curvatures is one of the difficulties encountered in the analysis of these shells. The finite element method is used here for bending analysis of truncated conoidal shells with parabolic directrix. The element used is an isoparametric doubly curved thin shell, and is rectangular. It has eight nodes and five degrees of freedom (DOFs) per node-three translations and two rotations. Quadratic isoparametric polynomials are used to express the element geometry and displacement parameters in terms of corresponding nodal values. The numerical problems using different boundary conditions are solved, and the results are compared with earlier results to show the effectiveness of this element even with a coarse mesh.

Finite element analysis of laminated composite paraboloid of revolution shells

Abstract A generalized formulation for the doubly curved laminated composite shell is attempted using eight-noded curved quadratic isoparametric finite elements with all three radii of curvature. The formulation is also applied to the isotropic material as a special case. In the present investigation, only the paraboloid of revolution is taken up for computing the deflections and stress resultants. Various parametric studies are carried out and the current results for both isotropic and laminated composite shells are compared with those available in the published literature. The shape functions are obtained from interpolation polynomial and the element stiffness matrices are formed on the basis of macromechanical analysis of laminates using the principle of minimum potential energy.

Stability and Strength of Composite Skew Plates Under Thermomechanical Loads

The buckling and postbuckling analysis of shear deformable composite skew plates subjected to combined uniaxial compression and uniform temperature rise has been carried out using the finite element method. The governing nonlinear finite element equation is posed as a sequence of linear eigenvalue problems, and each one of them is solved for different amplitudes of deflection to trace the thermal postbuckling path. A maximum strength criterion is used to identify the laminates that have failed in strength, and appropriate modifications are made to the stiffness matrix. The first-ply failure of laminates has also been predicted by Tsai-Hill and Tsai-Wu criteria. Postbuckling paths are traced for different boundary conditions of the plate. Specific numerical studies have been reported showing the effects of skew angle, initial uniaxial compression, and thickness-to-span ratio on the thermal postbuckling behavior of the eight-layered [45/-45/0/90 deg] s symmetric plate. The presence of secondary instability has been identified while tracing the postbuckling path.

Finite element free vibration analysis of conoidal shells

Doubly curved conoidal shells are increasingly used for various industrial structures. Conoidal shells are aesthetically appealing and, being ruled surfaces, provide ease of casting. The variation of curvature is the difficulty enountered in the analysis of these shells. The finite element method is used here for the analysis of generalized doubly curved shells and is applied to truncated and full conoids of different boundary conditions, aspect ratios and degrees of truncation. An eight-noded isoparametric finite element with five degrees of freedom per node, including three translations and two rotations, is utilized. The accuracy is checked by comparing the results obtained by the present analysis with those existing in the literature. Results are presented for different conoidal shells and a set of conclusions are arrived at based on a parametric study.

Theoretical and experimental studies on conoidal shells

Abstract The application of the finite difference method considering bending is studied to analyse conoidal shell structures. The solution can be obtained even with a microcomputer that is available in most design offices using less CPU time and memory space. Comparative theoretical results of a specific problem reveal that this method can be employed for a safe preliminary design of such structures. Furthermore, results of the experimental investigations of three conoidal shell specimens reveal the presence of arching action with increase in reinforcements in such shells.

Comparative analysis of folded plate structures

Abstract Folded plates are a very useful form of structure which has many advantages. Several methods are available for the analysis of this type of structure. Conventional methods are simple and easy, but they have the limitations of generality of application and precision. Rigorous methods are involved and some of these become costly due to the use of large-capacity computers. Two computer programs have been developed using the conventional Simpson and Whitney methods. Six different numerical problems solved by earlier investigators are considered to enable easy comparison of numerical results. It is shown that these methods give acceptable results for the preliminary analysis of folded plate structures.

Thermomechanical Postbuckling Response and First-Ply Failure Analysis of Doubly Curved Panels

The thermomechanical postbuckling response of graphite/epoxy multilayered doubly curved (spherical and elliptic paraboloid) shell panels having rectangular planform is obtained within the framework of the finite element method. The nonlinear equilibrium paths are predicted using the displacement control method and the temperature-dependent material properties are used in the analysis. The structural model is based on a first-order shear deformation theory incorporating geometric nonlinearities. The first-ply failure of laminates is predicted with the Tsai-Wu failure criterion. Specific numerical results are reported that show the effects of radius-of-curvature-to-span ratio and thickness-to-span-ratio on the stability and strength characteristics of doubly curved shell panels subjected to combined thermal and mechanical loads. Moreover, numerical results are presented showing the effect of temperature dependence of material properties on limit loads and snap-through response of shallow curved panels.

Bending analysis of doubly curved shell structures by finite element method

Abstract A generalized formulation for the doubly curved shells including all three radii of curvature has been attempted. The displacement fields u , v and w have been approximated with polynomials having 16 terms. Eigenvalue analysis has been performed on two isoparametric shell elements to check proper inclusion of rigid body modes. One hyperbolic paraboloid shell problem has been solved using the formulation with three different mesh sizes and with three different values of Poissons ratio. A comparative study of the results with those of earlier investigators and also of the effect of Poissons ratio on different shell actions has been made.