Discontinuity effects at cone-cone axisymmetric shell junctions

In this research, the free vibration analysis of lap joint laminated conical shell connected to laminated conical shell with adhesive layer for various boundary conditions are investigated. Based on the first-order shear deformation theory (FSDT), the main field equations of the analytical model are derived and the governing differential equations of laminated conical shell to laminated conical shell adherends lap joint are obtained for homogeneous and elasticity adhesive layers by using Hamilton principle method. Then, based on the generalized differential quadrature method (GDQM), the equilibrium equations of the structure adherends are investigated. The influence of the boundary conditions, the type of the composite materials and adhesive layer, the circumferential wave number, the length to radius ratio of the shell, and the length of overlap to length of shell ratio are studied. Furthermore, the thickness to radius ratio and the thickness of adhesive to thickness of shell ratio, as well as the various cone angles of conical shell on the natural frequency of laminated conical adherends shells connected to the conical shells with adhesive layer are investigated. For validation of the numerical results, the results are compared with the previous research and the comparisons show very good agreement. The numerical results show that with the increase of the internal shell and external shell of semi-angle, the non-dimensional frequency of lap joint connection of two laminated conical shells with adhesive layer decreased and increased, respectively. Furthermore, with the increase of the adhesive thickness to conical shell thickness ratio and lap joint length to length of conical shell ratio, the dimensionless natural frequency of the structure increased.

Bellows is a component in piping systems which absorbs mechanical deformation with flexibility. Its geometry is an axial symmetric shell which consists of two toroidal shells and one annular plate or conical shell. In order to analyze bellows, this study presents the finite element analysis using a conical frustum shell element. A finite element analysis is developed to analyze various bellows. The validity of the developed program is verified by the experimental results for axial and lateral stiffness. The formula for calculating the natural frequency of bellows is made by the simple beam theory. The formula for fatigue life is also derived by experiments. The shape optimal design problem is formulated using multiple objective optimization. The multiple objective functions are transformed to a scalar function by weighting factors. The stiffness, strength and specified stiffness are considered as the multiple objective function. The formulation has inequality constraints imposed on the fatigue limit, the natural frequencies, and the manufacturing conditions. Geometric parameters of bellows are the design variables. The recursive quadratic programming algorithm is selected to solve the problem. The results are compared to existing bellows, and the characteristics of bellows is investigated through optimal design process. The optimized shape of bellows is expected to give quite a good guideline to practical design.

In this research paper, an improved theory is used for buckling analysis of sandwich truncated conical shells with thick core and thin functionally graded material face sheets and homogeny core and with temperature-dependent properties. Section displacements of the conical core are assumed by cubic functions, and displacements of the functionally graded material face sheets are assumed by first-order shear displacements theory. The linear variations of temperature are assumed in the through thick. According to a power-law and exponential distribution the volume fractions of the constituents of the functionally graded material face sheets are assumed to be temp-dependent by a third-order and vary continuously through the thickness. In other words to get the strain components, the nonlinear Von-Karman method and his relation is used. The equilibrium equations are obtained via minimum potential energy method. Analytical solution for simply supported sandwich conical shells under axial compressive loads and thermal conditions is used by Galerkin’s solution method. Analysing the results show that the critical dimensionless axial loads are affected by the configurations of the constituent materials, compositional profile variations, thermal condition, semi-vertex angle and the variation of the sandwich geometry. Numerical modeling is made by ABAQUS finite element software. The comparisons show that the present results are in the good and better agreement with the results in the literature and the present finite element modelling.

In this paper free linear vibration of lattice composite conical shells will be investigated. Lattice composite conical shell consists of composite helical ribs and thin outer skin. A smeared method is employed to obtain the variable coefficients of stiffness of conical shell. The ribs are modeled as a beam and in addition to the axial loads, endure shear loads and bending moments. Therefore, theoretical formulations are based on first-order shear deformation theory of shell. For verification of the obtained results, comparison is made with those available in open literature. Also, using FEM software the 3D finite element model of composite lattice conical shell is built and analyzed. Comparing results of analytical and numerical analyses show a good agreement between them. Some special cases as variation of geometric parameters of lattice part, effect of the boundary conditions and influence of the circumferential wave numbers on the natural frequencies of the conical shell are studied. It is concluded, when mass and the geometrical ratio of the composite lattice conical shell do not change, increment the semi vertex angle of cone leads to increase the natural frequencies. Moreover for shell thicknesses greater than a specific value, the presence of the lattice structure has not significant effect on the natural frequencies. The obtained results have novelty and can be used for further and future researches.

In this paper, a study is carried out to investigate the stress concentrations at junctions of cylindrical-conical shell structures using the finite element method. A finite element solution is developed and used to model the structure. The solution utilizes curved finite elements that are capable to model the cylindrical and conical shell surfaces with high degree of accuracy. Elevated storage cylindrical-conical tanks and silos supported by "unyielding" stiff ring girders, which sit on a cylindrical skirt or on multi equally spaced columns, are analyzed. The opportunity is also taken to investigate the effects of various geometrical parameters, such as the conical angle, the height/radius ratio of the cylindrical shell, the location of the ring girder relative to the junction and the influence of adding ring stiffeners on the behavior of the structure. It is concluded that the geometrical discontinuity at the junction causes concentrations of compressive inplane as well as bending stresses. These stresses can be significantly reduced by either increasing the inclination angle of the conical bottom or by placing the ring girder closer to the junction.

This paper investigates the free vibration characteristics of truncated conical shells with variable thickness using the Haar wavelet method. Based on the Love first-approximation theory, the governing partial differential equations are formulated, which are transformed into ordinary differential equations using the separation of variables. The Haar wavelet discretization method is introduced to predict the dynamic characteristics of truncated circular conical shells with linearly and parabolically varying thickness. The present analysis is validated by comparing the numerical results with those available in the literature and very good agreement is achieved. The effects of geometrical parameters and boundary conditions on the vibration characteristics of conical shells with variable thickness are presented. The advantages of this method consist in its simplicity, fast convergence and high precision.

Background: Functionally graded material (FGM) is popularly recognized as promising material for modern engineering applications, which has gained attention of researchers due to its composition design and mechanical behaviour. FGM is the most suitable choice as a structural material for conical pressure vessel and requires detailed analysis for its mechanical behaviour. Objective: The design optimization of the rotating truncated conical shell made from FGM subjected to internal pressure (variable and constant) using Finite Element Method. Method: Using a commercially available finite element code, the effect of various parameters (such as cone angle, internal pressure, and angular velocity) on truncated conical shell was analyzed. The material properties and composition vary along the radial direction according to the exponential function. Results: Under the chosen circumstances 10¹ cone angle, 4-12MPa internal pressure, and 50 rad/sec rotational velocity were found most suitable. Conclusion: The results also demonstrated that chosen parameters (such as, cone angle, internal pressure, and rotational velocity) significantly affect the stresses working on conical shell. This requires careful selection while designing the conical pressure vessel. These optimization results are helpful for research community to design a conical shell pressure vessel using FGM.

The stress distribution along the intersection of offshore tubular T-joints under the action of axial and in-plane and out-of-plane (bending) brace loading has been investigated using degenerated shell elements. The ratios of through-thickness membrane to bending stress and bending to total stress have been obtained using a simple linear interpolation between the stresses on the inner and outer surfaces of the tube. The nominal brace stress and the maximum principal stress values have been used for stress concentration factor determination. The influence of thickness and other geometric parameters on the stress distribution along the intersection was investigated in two ways, viz., increasing the chord thickness while maintaining a constant brace thickness, and keeping the chord thickness constant while reducing the brace thickness.Comparison of the shell finite-element results obtained in this study with the semiloof thin-shell finite-element results of the University College, London (UCL), exhibits good agreement. Good agreement exists between the results of this study and the UCL parametric equations for the chord and the brace of the joint, with a maximum difference of about 7% on the braceside around the saddle position. Comparisons between the finite-element results and other known parametric equations for stress concentration factor with different diametral, wall thickness, and chord thickness and ratios also show good agreement. A comparison of the results obtained from the finite-element analysis and the experimental results of the Canadian Cooperative Fatigue Studies Program, carried out at Memorial University of Newfoundland and University of Waterloo, is also made. Key words: stress distribution, finite-element analysis, stress concentration factors, membrane stress, bending stress, tubular T-joints.

This paper presents the finite element simulation of stress distribution features of 3D layer-to-layer angle-interlock woven composite undergoing three-point bending cyclic loading. With the finite element analysis model, a microstructure shell element model of the woven composite at yarn level was established to calculate the fatigue behaviors and stress distribution during cyclic loading. The stress distributions in the warp, weft yarns, and the resin regions have been calculated to show the stress difference in the woven composite. It has been observed that the warp yarns share the most part of the stress or loading, i.e. the strength warp yarn is more important than that of the weft yarn for the fatigue design. In addition, the stress distributions at the locations where the weft yarns crossover the warp yarns have been investigated. The stress degradations of the top and bottom surface of the woven composite panels were also compared with those in experimental and good agreement was found. With the stress distribution in the woven composite, the method of improving the fatigue damage tolerance was expected to be developed.

Purpose: To analyze the stress distribution and the direction of force in external hexagonal implant with crown in three different angulations. Materials and Methods: A total of 60 samples of geometric models were used to analyze von Mises stress and direction of force with 0-, 5-, and 10-degree lingual tilt. Von Mises stress and force distribution were evaluated at nodes of hard bone, and finite element analysis was performed using ANSYS 12.1 software. For calculating stress distribution and force, we categorized and labeled the groups as Implant A1, Implant A2, and Implant A3, and Implant B1, Implant B2, and Implant B3 with 0-, 5-, and 10-degree lingual inclinations, respectively. Inter- and intra-group comparisons were performed using ANOVA test. A p-value of ≤0.05 was considered statistically significant. Results: In all the three models, overall maximum stress was found in implant model A3 on the implant surface (86.61), and minimum was found on model A1 in hard bone (26.21). In all the three models, the direction of force along three planes was maximum in DX (0.01025) and minimum along DZ (0.002) direction with model B1. Conclusion: Maximum von Mises stress and the direction of force in axial direction was found at the maximum with the implant of 10 degrees angulation. Thus, it was evident that tilting of an implant influences the stress concentration and force in external hex implants.

We investigated and compared the stress distribution within one- and two-piece mini-implants for overdentures with three different attachments (ball, Locator, and magnet) and two different diameters using three-dimensional finite element (3D FE) analysis and a monotonic bending test. The goal was to identify the most beneficial implant attachment system design for mini-implant overdentures with a lower risk of implant fracture. Twelve 3D FE models simulating a mandible segment with one- and two-piece mini-implants with different attachment systems, diameters, and overdentures were created using three-dimensional computer-aided design (CAD) software. Vertical and oblique forces (45° to the longitudinal axis of the implant) of 100 N were applied to the dentures. The stress distribution was analyzed. A bending test was performed on a mini-implant (Locator, 2.4 mm) using a testing machine to quantify the load at yield stress. One-piece mini-implants showed lower maximum stress compared to two-piece mini-implants. Among the three designs, the magnet attachment systems showed the maximum stress. The maximum von Mises stress occurred at the neck of the implants, which was surrounded by cortical bone in all models, and under both loading conditions. Focusing on the attachments and one- and two-piece designs of mini-implant overdentures using CAD models to reduce confounding factors affecting the stress distribution, we concluded that one-piece mini-implants tended to show lower stress compared to two-piece mini-implants. Mini-implant overdentures with Locator and ball attachments demonstrated lower stress within the implants compared to those with magnet attachments under vertical and oblique loading conditions.

Simulations based on finite element analysis (FEA) have attracted increasing interest in dentistry and dental anthropology for evaluating the stress and strain distribution in teeth under occlusal loading conditions. Nonetheless, FEA is usually applied without considering changes in contacts between antagonistic teeth during the occlusal power stroke. In this contribution we show how occlusal information can be used to investigate the stress distribution with 3D FEA in lower first molars (M(1)). The antagonistic crowns M(1) and P(2)-M(1) of two dried modern human skulls were scanned by μCT in maximum intercuspation (centric occlusion) contact. A virtual analysis of the occlusal power stroke between M(1) and P(2)-M(1) was carried out in the Occlusal Fingerprint Analyser (OFA) software, and the occlusal trajectory path was recorded, while contact areas per time-step were visualized and quantified. Stress distribution of the M(1) in selected occlusal stages were analyzed in strand7, considering occlusal information taken from OFA results for individual loading direction and loading area. Our FEA results show that the stress pattern changes considerably during the power stroke, suggesting that wear facets have a crucial influence on the distribution of stress on the whole tooth. Grooves and fissures on the occlusal surface are seen as critical locations, as tensile stresses are concentrated at these features. Properly accounting for the power stroke kinematics of occluding teeth results in quite different results (less tensile stresses in the crown) than usual loading scenarios based on parallel forces to the long axis of the tooth. This leads to the conclusion that functional studies considering kinematics of teeth are important to understand biomechanics and interpret morphological adaptation of teeth.

Finite element analyses on transverse impact behaviors of 3-D circular braided composite tubes with different braiding angles

The equations for integral instantaneous characteristics of composite materials consisting of elastoplastic fibers and matrix are derived based on the known hypotheses of uniform strain or stress fields. The constitutive relations for a layered shell are obtained. The numerical algorithm elaborated is used to solve the stability problem for conical boron-aluminum shells under external pressure and axial compression. It is shown that the shells of medium thickness lose their stability under loads whose magnitude depends on the plasticity of the binder. The plasticity has a decisive influence on the choice of the optimum directions of reinforcement. If the parameters of a shell are such that the buckling occurs beyond the elastic limit, the shell must be reinforced in the direction of precritical stresses. However, this is possible only upon separate action of loads.

Peri-implant stress distribution assessment of various attachment systems for implant supported overdenture prosthesis by finite element analysis – A systematic review