4-node Shell Element Research Articles

Fatigue assessment of fillet welded doubling plates using different methods

Analysis results using finite elements are compared with strain measurements and laboratory fatigue testing of doubling plates used in floating production platforms. Circular and quadratic doubling plates of thickness 10 mm with diameter and length equal to 150 mm fillet welded to a main plate of thickness 20 mm were fatigue tested. The testing was performed until crack growth through the plate thickness and the number of test cycles was compared with design standards. Finite element analyses of the doubling plates were performed using different methods for hot spot stress derivation in combination with relevant S-N curves. Analyses were performed using 8-node shell elements and 20-node solid elements. Hot spot stresses were based on calculated surfaces stresses at the weld toe. Also stresses through the thickness of the main plate were used for assessment of the hot spot stress. For purpose of analyses the main attention was made to the weld toe. However, the main reason for performing the fatigue testing was related to concern for crack growth from the weld root. This failure mode was found to be less critical than fatigue crack growth at the weld toe. The results from this work are being used for developing more reliable analysis methods to be included in design standards.

On transient responses of sandwich plate with cutout using FEM

In the present research work, time-dependent transverse deflection responses of a sandwich composite plate with cutout have been analyzed by using lower-order theory in conjunction with the finite element approach. Initially, the sandwich structure with the cutout (square, pentagonal, hexagonal, and circular) is developed in the ANSYS platform using ANSYS parametric design language (APDL) code. The necessary material properties of the sandwich structure (face sheet and core) are assigned. The developed model has been discretized using 8 noded shell element (Shell 281). The structure is now assigned a simply supported end condition and uniformly distributed loading (UDL). Now, the numerical model’s accuracy is evaluated by comparing the simulated results to previously published literature’s results. The developed simulation model has been used further to investigate the effect of cutout ratios, cutout shape (square, pentagon, hexagon and circle) and core to face thickness ratio on the transient response of a square sandwich panel via new examples. The findings of the examples are analyzed and discussed in detail.

Traveling wave resonance analysis of flexible spur gear system with angular misalignment

The aero-engine spur gear system is often designed as thin rim structure due to lightweight consideration, which leads to traveling wave resonance phenomenon when spur gear system has angular misalignment during operation. This paper mainly analyzes traveling wave resonance phenomenon of aero-engine angular misalignment thin rim spur gear system. Time-varying mesh stiffness (TVMS) of spur gear system is calculated by loaded tooth contact analysis (LTCA) method, angular misalignment is introduced into spur gear system, and axial component of TVMS is obtained by the projection method. Flexible gear foundations are simulated by 8-node shell element and rotational shafts are simulated by Timoshenko beam element, combined with axial stiffness, the dynamic model of flexible spur gear system is established. Simulation results are compared with the references and finite element (FE) model, which proves the accuracy of the proposed method. The analysis results of angular misalignment spur gear system traveling wave resonance phenomenon show that during the operation of spur gear system, angular misalignment produces axial excitation, which excite nodal diameter vibration of gear foundations, and traveling wave resonance phenomenon appears at nodal diameter vibration resonance speed. The effects of misalignment angle, web thickness and gear torque on spur gear system traveling wave resonance amplitude and resonance speed are discussed. The research of aero-engine angular misalignment spur gear system provides theoretical basis for structural design and fault diagnosis of aero-engine gear systems.

A solution for free vibration of rotating hybrid multiscale nanocomposite conical shell

In the present investigation, first-order shear deformation theory (FSDT) is employed to conduct free vibration analysis of hybrid CNT-fiber nanocomposite conical shells using finite element approach. The effective material properties of this three phase nanocomposite is computed using Halpin- Tsai and Micro-mechanics model approach. The Lagrange’s equation of motion is used to derive the equilibrium equations of the rotating carbon nanotube – fibre nanocomposite conical shell wherein the nonlinearity due to rotation is also introduced. The Coriolis effect is neglected because of the moderate rotational speed of the shell. Finite element code is developed using eight noded isoparametric shell element and the same is validated with some literature to analyse the effect of twist angle, length to thickness ratio, aspect ratio, weight fraction of CNTs, and rotational speed on the fundamental frequency. The effect of such parameter on the mode shapes of the three phase nanocomposite shell are also presented here.

Spatial Numerical Simulation of Locally Corroded Steel Plate Girder with Various End Panels

Field inspections indicate that corrosion damages steel bridge girders more at the ends as compared to the central region. Any significant loss of metal around the bearing region of the girder may cause an abrupt change of failure behavior and strength loss. The present numerical study is focused to evaluate the response of local corrosion damage at steel plate girder, with different end panels, that is, no end post, nonrigid, and rigid end post. Local corrosion damage was considered by reducing the bearings stiffener and adjacent web uniformly for a maximum damage depth of 100 mm with various corrosion damage levels (i.e., 75%, 50%, and 25%). The numerical analysis was performed on a computer package ABAQUS, using modified Riks analysis. A 4‐node shell element (S4R) with reduced integration was used to simulate the model. The study concludes that local corrosion damage is more critical in nonrigid end post than in rigid end post. Furthermore, the steel girder with no end post is more susceptible to crippling failure due to local corrosion damage as compared to the other types of end post.

A solution to free vibration of rotating pretwisted hybrid CNTs multiscale functionally graded conical shell

In the present study, the free vibration analysis of multiscale functionally graded (FG) carbon nanotube (CNT)–metal–ceramic composite conical shells is conducted using finite element methodology. Using first-order shear deformation theory (FSDT) strains are computed and an eight noded isoparametric shell element is used in the present formulation. Dynamic equation is derived using Lagrange’s equation of motion for moderate rotational speeds wherein Coriolis effect is neglected. The finite element code is developed and validated with the existing literature to analyze the effects of power law index, weight fraction of CNTs, length to thickness ratio, aspect ratio, twist angle and rotational speeds on fundamental natural frequency. Mode shapes of both twisted and untwisted conical shells under varying rotating conditions are also presented.

Static and free vibration analyses of moderately thick hyperbolic paraboloidal cross ply laminated composite shell structure

The main objective of this paper is to investigate the response behaviour of moderately thick hyperbolic paraboloidal laminated shells using C0 finite element formulations based on Higher order Shear Deformation Theory (HSDT). The mathematical model of HSDT includes the thickness co-ordinate to radius of curvature ratio (z/R) as well as zero shear conditions at free surfaces of the shell. The finite element equations have been developed using eight noded isoparametric shell element with seven degrees of freedom per node. The Jacobian matrix used in the finite element procedure is formulated by considering the curvilinear coordinates of the shell element. The accuracy of the present HSDT is validated by comparing the obtained results with those available published 2D and 3D elasticity solutions. An extensive parametric study on static and free vibration analyses of moderately thick hyperbolic paraboloidal laminated shells has been carried out to study the performance of shell for various geometric configurations.

Numerical Evaluation on Improvement Performance of Waved Connection to Reduce Damage on Buried Gas Pipeline

One of the major challenges for the oil and gas industry is to keep buried metal pipes safe from faulting. This paper discusses about a solution to keep buried pipes safe. In this study, after examining the different dimensions of the effect of wave connection on improving the performance of buried metal pipes, by changing the geometric shape of the wave connection such as doubling it, the behavior of the pipe is greatly improved. Waved connections, by their local deformation, create a rotational joint in a limited area so that other parts of the pipe remain intact. In this paper, the behavior of buried pipes due to slip direction fault displacement by modelling with Abacus software version 2017 and selection of 4-node shell element and 8-node shell element have been used for pipe and soil modelling, respectively. In this paper, by comparing to a single waved connection with a double waved connection, the performance of the pipe due to the faulting phenomenon was evaluated. The results show the improvement of the excellent performance of the double joint by reducing the plastic strain values. In addition to increasing the ductility of the pipe, the double connection has been able to reduce the strain values by about 50% compared to the single connection. In general, this paper shows that the use of wave connections can significantly increase the level of safety of buried gas pipelines without increasing the cost.

Transient dynamic response of doubly curved laminated composite shells under pulse loading

Transient response behavior of laminated doubly curved shells with varying geometry and boundary conditions subjected to various time-dependent pulse loads is investigated using Higher order Shear Deformation Theory (HSDT) in the present study. The ratio of thickness co-ordinate to radius of shell (z/R) is incorporated in the mathematical formulation based on HSDT. The condition of zero transverse shear stresses at free surfaces of laminated shell is also included in the displacement function. A C0 finite element formulation using eight noded isoparametric shell element with seven degrees of freedom per node is applied to evaluate the dynamic response of shells. Three types of pulse loading such as sine, triangular and rectangular pulses are considered for the present investigation. Newmark's β method is applied to solve the dynamic equilibrium equation of the shells. The accuracy of the present analysis is examined by comparing the results obtained with those available in the published literature. Several numerical examples are illustrated to show the effects of pulse loading and boundary condition on the central displacement and stresses of laminated composite shells.

Locking-free robust finite element approximation of thin shell-like structures

In the structural analysis of thin elastic structures using standard FEMs within the poor approximation space, the numerical results may suffer from the quality deterioration called the locking phenomenon. This situation becomes more crucial for the structures with non-vanishing curvatures, such as arch- and shell-like bodies, owing to the additional membrane constraints. In addition, the choice of unsuitable shear correction factor (SCF), in dimen-sionally-reduced first-order analysis models, may become an additional source for the quality deterioration. In this context, we here propose a locking-free robust finite element approximation for the robust structural analysis of shell-like structures, by improving the degenerated 8-node shell element. In order to completely overcome the quality deterioration according to the thickness reduction, we combine the reduced integration (RI) and the modified shear correction factor.

An improved quadrilateral shell element based on the Hu\u2013Washizu functional

In this paper a robust and effective 4-node shell element for the structural analysis of thin structures is described. A Hu–Washizu functional with independent displacements, stress resultants and shell strains is the variational basis of the theory. Based on a previous paper an additional interpolation part using quadratic shape functions is introduced for the independent shell strains. Especially for unstructured meshes this leads to an improved convergence behavior. The expanded element formulation proves to be insensitive to mesh distortion. Another well-known feature of the mixed hybrid element is the robustness in nonlinear applications with large deformations.

Buckling analysis of functionally graded thin square plates with triangular cut-out subjected to uni-axial loads

In this article, the buckling behaviour of simply supported functionally graded (FG) thin square plates with triangular cut-out subjected to mechanical loading is investigated. Both uniform and non-uniform (linear triangle and trapezoidal) in-plane uniaxial compressive loadings are considered. Finite element method based on first order shear deformation theory (FSDT) is used to find out the critical buckling loads with the help of ANSYS – a commercial finite element software. Eight noded shell element with six degrees of freedom at each node is used for discretization. The material properties of the plates are assumed to vary along the thickness according to a simple power law distribution in terms of volume fraction exponent. The effects of volume fraction exponent and cut-out size for the various types of loads considered are presented. Finally, from the results it is observed that the buckling load capacity decreases with the increase in volume fraction exponent and cut-out size for the considered types of loading

Investigation of Crack Repair in Orthotropic Composite by Piezoelectric Patching

Abstract This paper presents the investigation of a crack repair in a composite plate using piezoelectric smart material, which is also called as active repair. Composite plate with crack is modeled by a finite element method. An 8-node structural shell element is used to discretize composite material, and the 8-node coupled-field element is used for the modeling of the piezoelectric patch. The repair in the cracked composite plate is modeled and analyzed under both static and dynamic loading conditions. The unimorph and bimorph patching are used for active repair. Effectiveness of the patch repair is measured in terms of stress field near the crack tip. The usefulness of unimorph and bimorph patching is compared in three different cases, namely (i) passive, (ii) active and (iii) without patching. A significant reduction in the equivalent stress at the crack tip of the composite plate is observed because of repair by unimorph and bimorph active patching. Bimorph patching presents a greater reduction in the stress level near to discontinuity

Study of Reserved Strength Capacity of Concrete Shell

Hyperbolic cooling towers have become the design standard for all natural-draft cooling towers because of their structural strength and minimum usage of material. The hyperbolic shape is particularly suited to cooling tower construction as the wide base provides a large space for the water and cooling system. As the tower widens out at the top, it supports the turbulent mixing as the heated air makes contact with the atmospheric air. Hyperbolic cooling tower is a tall structure with shells subjected to dead load and wind load. In absence of ground motion, wind becomes the major factor. In this study, 2 major models are studied with I and V column support. Each model is further divided into 2 models, i.e. one with SHELL element and another with SOLID element. All models were modelled and analyzed in ANSYS. The wind loads on these cooling tower have been calculated in the form of pressure by using the circumferentially distributed design wind pressure coefficients as given in IS: 11504 - 1985 code along with the design wind pressures at different levels as per IS: 875 (Part 3) - 1987 code. The analysis has been carried out using 8 noded shell element (SHELL281), 8 noded solid element (SOLID185) and 20 noded solid element (SOLID 186).

Robust four-node elements based on Hu\u2013Washizu principle for nonlinear analysis of Cosserat shells

Mixed 4-node shell elements with the drilling rotation and Cosserat-type strain measures based on the three-field Hu–Washizu principle are proposed. In the formulation, apart from displacement and rotation fields, both strain and stress resultant fields are treated as independent. The elements are derived in the framework of a general nonlinear 6-parameter shell theory dedicated to the analysis of multifold irregular shells. The novelty of the developed elements stems from the fact that the measures of assumed strains and stress resultants are asymmetric. The original interpolation of drilling and bending components of strains and stress resultants is proposed. In the formulation of new mixed elements, two variants of the interpolation of membrane components are used and interpolation of the independent fields is defined in the natural or skew coordinates. Accuracy and efficiency of the developed elements are tested in several linear and nonlinear numerical examples. It is shown that smaller number of independent parameters in the interpolation of membrane components gives more accurate results. The proposed mixed 4-node elements enable the use of large load steps in nonlinear computations. Moreover, they require significantly less equilibrium iterations than other shell elements formulated in the 6-parameter shell theory.

3D simulation of transversely isotropic laminated composites in RTM using poromechanics

In the present paper we are trying to establish a 3D simulation framework for Resin Transfer Molding for a laminated preform using the already developed porous media theory for composite materials process simulation purposes. The aim here is to implement the process phenomena, such as coupling of sub-processes that are happening simultaneously, in a full 3D description of the problem. For this purpose, an 8-node solid shell element is employed to be able to handle complex 3D stress-strain states. The development is exemplified considering RTM process where the main focus of the modeling will be on the flow advancement into fiber preform and flow front capturing. To this end, the theory of two-phase porous media is used along with assuming hyper-elastic material response for the fiber bed to formulate the problem. A finite element formulation and implementation of the two-phase problem is developed, and the results are presented accordingly.

A nonlinear quadrilateral thin flat layered shell element for the modeling of reinforced concrete wall structures

In this article, a simple and accurate quadrilateral thin flat layered shell element formulation for the nonlinear analysis of reinforced concrete (RC) wall systems under static and cycling loads is presented. The 4 node shell element, with 6 degree of freedom (DOF) per node (3 displacements and 3 rotations) is created by superposing the quadrilateral layered membrane element with drilling degrees of freedom (12 DOF, 2 displacement and 1 rotation per node) developed by Rojas et al. (Eng Struct 124:521–538, 2016), and the Discrete Kirchhoff Quadrilateral Element (12 DOF, 1 displacement and 2 rotations) formulated by Batoz and Tahar (Int J Numer Methods Eng 18(11):1655–1677, 1982), to model the in-plane and the out of plane bending behavior of the shell element, respectively. In addition, to model the complex behavior and coupling of the axial, flexural and shear behavior, observed in complex RC wall structures, the transversal section of the shell element consists of a layered system of fully bonded, smeared steel reinforcement and smeared orthotropic concrete material with the rotating angle formulation. The formulation used a tangent stiffness matrix approach, which include the coupling of membrane and bending effects. For verification, the shell element formulation is used to model a set of experimental results for T-shaped RC walls that are available in the literature. The proposed element is robust, simple to implement, and it can predict the global results (load vs. displacement and maximum capacity) and also the local behavior (vertical strain at the base level along the web and the flange) observed in RC wall structures.

Master S-N Curve-Based Fatigue Life Assessment of Steel Bridges Using Finite Element Model and Field Monitoring Data

The accuracy of fatigue life assessment for the welded joint in a steel bridge is largely dependent on an appropriate [Formula: see text]-[Formula: see text] curve. In this paper, a master [Formula: see text]-[Formula: see text] curve-based fatigue life assessment approach for the welded joint with an open-rib in orthotropic steel bridge deck is proposed based on the finite element model (FEM) and field monitoring data from structural health monitoring (SHM) system. The case studies on fatigue life assessment by use of finite element analysis (FEA) for constant-amplitude cyclic loading mode and field monitoring data under variable-amplitude cyclic loading mode are addressed. In the case of FEA, the distribution of structural stress at fatigue-prone weld toe is achieved using 4-node shell element model and then transformed into equivalent structural stress by fracture mechanics theory. The fatigue life of the welded joint is estimated with a single master [Formula: see text]-[Formula: see text] curve in the form of equivalent structural stress range versus the cycles to failure. In the case of monitoring data-based fatigue life assessment, the daily history of structural stress at diaphragm to U-rib is derived from the raw strain data measured by the instrumented fiber Bragg grating (FBG) sensors and transformed into equivalent structural stress. The fatigue life of the investigated welded joint is calculated by cyclic counting method and Palmgren–Miner linear damage cumulative rule. The master [Formula: see text]-[Formula: see text] curve method provides an effective fatigue life assessment process, especially when the nominal stress is hard to be defined. A single master [Formula: see text]-[Formula: see text] curve will facilitate to solve the difficulty in choosing a proper [Formula: see text]-[Formula: see text] curve which is required in the traditional fatigue life assessment methods.

Study on Harmonic Analysis of Functionally Graded Plates Using Fem

This paper presents the harmonic and vibration analysis of functionally graded plates using the finite element method. Initially, the plates are assumed isotropic and the material properties of it are assumed to vary continuously through their thickness direction according to a power-law distribution of the volume fractions of the plate constituents. The four noded shell element is used to analyse the functionally graded plates. Four functionally graded plates-Al/Al<sub>2</sub>O<sub>3</sub>, Al/ZrO<sub>2</sub>, Ti–6Al–4V/Aluminium oxide, and SUS304/Si<sub>3</sub>N<sub>4</sub> are considered in the study, and their results are obtained so that the right choice can be made in applications in high temperature environment and in reducing the vibration amplitudes in applications such as aircrafts, rockets, missiles, etc. Numerical results for the natural frequency and harmonic response amplitude are presented. Results are compared and validated with available results in the literature. Effects of boundary conditions, material and damping on natural frequency and harmonic response of the functionally graded plates are also investigated.

A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells

In this paper, the thermal buckling behavior of functionally graded plates and cylindrical shells is investigated. By considering a modified First order Shear Deformation Theory, the governing equations are elaborated. The kernel idea of the proposed model consists on assuming a parabolic distribution of the transverse shear strains across the shell thickness and imposing a zero condition of the transverse shear stresses on the top and bottom surfaces of the shell structure. Four nodes shell elements are adopted to solve the thermal buckling problem. The material properties are assumed to change continuously through the thickness according to a power-law distribution. In order to highlight the potentials of the present formulation, numerical investigations are conducted and compared with results available from the literature. The computation of the critical buckling temperature of structures under non-uniform temperature rise is based on Gauss numerical integration. The effects of material compositions, power law index, thermal loading, boundary conditions and geometrical parameters of shells on the thermal buckling behavior of FGM structures are also examined.