4-node Shell Research Articles

Reinforcing Fibre Reinforced Polymer Bridge Decks with Steel Rods

Fibre reinforced polymer (FRP) bridge decks have become an innovative alternative and they have offered many advantages and this has been increasing attention for applications in not only reinforcement of existing bridges decks but also construction of new bridges decks. The advantages of these FRP decks are; lightweight, high-strength FRP materials, corrosion resistance. However, this high strength deck is not ductile. In this study, the behaviour of hybrid FRP-steel decks are investigated. All FRP decks was analysed with the commercial package ABAQUS. In the FE model, the webs and flanges were discretised by 4 nodes shell elements. A full composite action between the steel and the FRP composite was assumed in the FE analysis because the bond-slip behaviour was unknown at that time. The performance of the proposed hybrid FRP deck panel was evaluated by means of FE analysis.

Properties of numerical solution of the deformation and stability problem in shallow conical shells under external pressure

The paper presents an analysis of a numerical solution in the ANSYS software to three problems related to determination of deformations and stability of closed shallow conical shells under external pressure: 1) linear (bifurcation) problem of determining the critical pressure; 2) geometrically non-linear problem of shell deformation and buckling to determine the limit pressure using axisymmetric finite elements (FE); 3) solution to the same problem as set out in 2, yet using 4-node shell elements. The solutions presented in the paper concern the stationary state of a simply supported and fixed shell. Shallow conical shells are applied as load bearing and protective elements of bridge structures.

A 4-node quadrilateral flat shell element formulated by the shape-free HDF plate and HSF membrane elements

Purpose The purpose of this paper is to propose an efficient low-order quadrilateral flat shell element that possesses all outstanding advantages of novel shape-free plate bending and plane membrane elements proposed recently. Design/methodology/approach By assembling a shape-free quadrilateral hybrid displacement-function (HDF) plate bending element HDF-P4-11β (Cen et al. 2014) and a shape-free quadrilateral hybrid stress-function (HSF) plane membrane element HSF-Q4θ-7β (Cen et al. 2011b) with drilling degrees of freedom, a new 4-node, 24-DOF (6 DOFs per node) quadrilateral flat shell element is successfully constructed. The trial functions for resultant/stress fields within the element are derived from the analytical solutions of displacement and stress functions for plate bending and plane problems, respectively, so that they can a priori satisfy the related governing equations. Furthermore, in order to take the influences of moderately warping geometry into consideration, the rigid link correction strategy (Taylor 1987) is also employed. Findings The element stiffness matrix of a new simple 4-node, 24-DOF quadrilateral flat shell element is obtained. The resulting models, denoted as HDF-SH4, not only possesses all advantages of original HDF plate and HSF plane elements when analyzing plate and plane structures, but also exhibits good performances for analyses of complicated spatial shell structures. Especially, it is quite insensitive to mesh distortions. Originality/value This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop low-order mesh-distortion resistant flat shell elements.

Piezoelectric Co-Rotational 3-Node Shell Element

Geometrically nonlinear FE-analysis of active piezoelectric thin-walled shell structures, based on a Co-Rotational (CR) formulation and the Cell-Smoothed Discrete-Shear-Gap 3-node shell element (CS-DSG3) is presented in this study. The electric potential across the thickness of piezolayers is approximated by a linear function. The basic assumption of the applied Co-Rotational (CR) FEM formulation is that translations and rotations are finite, whereas the strains are small. Large rotation theory is used to update the rotational degrees of freedom. The proposed formulation is tested by means of the originally developed program. A set of piezoelectric coupled static linear and nonlinear cases are studied and the obtained results are compared with those available in the literature. A very good agreement of the results is noted, whereby the numerical effort could be reduced and numerical stability improved compared to other geometrically nonlinear FEM formulations.

The MITC4+ shell element and its performance

The objective in this paper is to improve the performance of the 4-node MITC quadrilateral shell finite element, referred to as the MITC4 element (Dvorkin and Bathe, 1984). We propose a new MITC4 shell element, the MITC4+ element, in which the mid-surface membrane strain components are assumed using the concept of the MITC method. The tying membrane strains are obtained from four triangular domains which subdivide the mid-surface of the 4-node quadrilateral shell element. This approach alleviates locking that can happen when the MITC4 shell elements are geometrically distorted in curved geometries. Several basic tests including the isotropy, zero energy mode, and patch tests are performed. Through the solution of various shell problems, the convergence behavior of the MITC4+ shell element is studied to show the improvements reached.

Numerical studies on CFRP strengthened steel circular members under marine environment

The durability of carbon fibre reinforced polymer (CFRP) strengthened steel circular hollow section (CHS) members has now become a real challenge to researchers. In addition, various parameters that may affect the durability of such members have not been revealed yet. This paper presents brief experimental results and the first finite element (FE) approach of CFRP strengthened steel CHS beams conditioned in simulated sea water, along with an accelerated corrosion environment at ambient (24 ± 4 °C) and 50 °C temperatures. The beams were loaded to failure under four-point bending. It was found that the strength and stiffness reduced significantly after conditioning in an accelerated corrosion environment. Numerical simulation was implemented using the ABAQUS static general approach. A cohesive element was utilised to model the interface element and an 8-node quadrilateral in-plane general-purpose continuum shell was used to model CFRP elements. A mixed mode cohesive law was deployed for all the three components of stresses in the proposed FE approach, which were one normal component and two shear components. The validity of the FE models was ascertained by comparing the ultimate load and load vs deflection response from experimental results. A range of parametric studies were conducted to investigate the effects of bond length, adhesive types, thickness and diameter of tubes. The results of parametric studies indicated that the adhesive with high tensile modulus performed better and durability design factors varied from section to section.

Strength and Stability Analysis of Load-bearing Structures of Evolution Tower with Allowance for Actual Positions of Reinforced Concrete Structural Members

The distinctive paper is devoted to strength and stability analysis of loadbearing structures of Evolution Tower (high-rise 54-storey building) with allowance for actual positions of reinforced concrete structural members (columns and walls). Finite element method (FEM) is used for structural analysis. The authors present formulations of problems, governing equations, information about basic three-dimensional finite element models (so-called “design” (ideal) model, the first “actual” model (taking into account the deviations of positions of columns from the project) and the second “actual” model (taking into account the deviations of positions of walls from the project)) of the coupled system “Evolution Tower – foundation” within ANSYS Mechanical software and their verification, numerical approach to structural analysis and corresponding solvers. Finite element models include mainly 4-node structural shell elements (suitable for analyzing foundation slabs, floor slabs and load-bearing walls) and three dimensional 2-node beam elements (suitable for analyzing beams and columns), special spring-damper elements and multipoint constraint elements. Detailed finite element mesh on the bottom foundation slab is agreed with the location of piles. The advanced model of Prof. Yu.K. Zaretsky is used for approximation of soil behavior. Construction sequence and various types of nonlinearities are taken into account. The results of modal analysis, static and dynamic analysis with various load combinations (gravity load, façade load, dead (constant) loads, temporary loads, wind load, snow load, crown load etc.) are considered, the results of the regulatory assessment of the strength of structures (obtained with the use of corresponding software in accordance with design codes of the Russian Federation) are under consideration as well. The corresponding displacements, stresses, natural vibration frequencies can be used for research and development of the correct monitoring method of the foundation and load-bearing structures of a high-rise building.

Analytical Study of Double Flight Stair Slab without Floor Landing

This paper presents an analytical analysis of double flight stair slab without floor landings with boundary condition fixed at extreme edges. The analysis is based upon finite element method using ANSYS software. The staircase specimen for one storey height of 3m, with mid landing height each at 1.5m from the floor and 100mm thick waist slab has been chosen for a horizontal projection of 2.475m attached with mid landings. The specimen has discretized in to 54 numbers of four noded structural shell elements (shell 181). The specimen has tested under incrementally applied uniformly distributed load over the complete area. Critical value of bending moment and deflection of support arrangement has been obtained. Variation in moments and deflections at critical locations, along the stair slab model has been presented in the graphical form.

Structural Stability and Dynamics of FGM Plates Using an Improved 8-ANS Finite Element

I investigate the vibration and buckling analysis of functionally graded material (FGM) structures, using a modified 8-node shell element. The properties of FGM vary continuously through the thickness direction according to the volume fraction of constituents defined by sigmoid function. The modified 8-ANS shell element has been employed to study the effect of power law index on dynamic analysis of FGM plates with various boundary conditions and buckling analysis under combined loads, and interaction curves of FGM plates are carried out. To overcome shear and membrane locking problems, the assumed natural strain method is employed. In order to validate and compare the finite element numerical solutions, the reference results of plates based on Navier’s method, the series solutions of sigmoid FGM (S-FGM) plates are compared. Results of the present study show good agreement with the reference results. The solutions of vibration and buckling analysis are numerically illustrated in a number of tables and figures to show the influence of power law index, side-to-thickness ratio, aspect ratio, types of loads, and boundary conditions in FGM structures. This work is relevant to the simulation of wing surfaces, aircrafts, and box structures under various boundary conditions and loadings.

A Comparative Study on Passive Vibration Damping in Thin Carbon Nanotube Based Hybrid Composite Spherical Shell Panel

The present article deals with the vibration problem associated with thin carbon fiber reinforced composite (CFRC) shell structures that can be mitigated by addition of carbon nanotubes (CNTs) in the polymer matrix phase of such CFRC structures. Mori-Tanaka in conjunction with strength of material method has been employed to obtain the elastic properties of such hybrid composite. Shell structure is discretized by eight noded shell element having five degree of freedom at each node where stress resultant-type Koiter's shell theory is applied. Impulse response using Duhamel integral and frequency response analysis have been carried out to analyze the damping phenomena of hybrid composite structure considering Raleigh damping. Results revealed that there are profound influence of carbon nanotube content on the dynamic response of the system. It is also found that the both the damping and stiffness of the structure is increased by the inclusion of carbon nanotubes.

Analysis of Stress Concentration in Orthotropic Laminates

The current paper presents a comprehensive finite element analysis on stress concentration in orthotropic laminates. This research investigates the Stress Concentration Factor (SCF) in isotropic and orthotropic plates due to presence of a central cutout with respect to ply orientation angle (θ). The numerical simulations are carried out by using an 8 node shell element in ANSYS APDL environment. It is established from the simulations that the SCF is dependent upon the orientation the fibers. For orthotropic laminates, SCF depends on material properties. It increases with increase in Ey/Ex ratio and decreases with increase in μxy.

Effect of Web Opening on the Ultimate Capacity of Steel Plate Girders under Two Points Load

The structural behavior of steel plate girders with web opening is investigated in this study. An experimental and theoretical investigation of plate girders with circle and square openings in the web was conducted. The experimental work included testing of seven plate girder specimens under two point loads. Three specimens were tested to observe the influence of the circular web opening. The influence of the presence of square web openings was studied by testing other three specimens. The last one was tested without opening as a reference (control) specimen. These specimens had the same dimensions. The experimental results showed that the ultimate load capacity of the girders decreases with increasing the opening size, and the position of plastic hinge depends on the size of hole. Three-dimensional nonlinear finite element analysis has been used to conduct the numerical investigation of the structural behavior of plate girders with web opening. ANSYS (version 12.0) computer program was used in this study. Four- nodes shell element (SHELL 181) was used to represent the steel plate. The proposed finite element model has been used to carry out a parametric study to investigate the effects of two parameters; web slenderness and flange stiffness ratios, on the ultimate load capacity of plate girders with circular web openings.

An Explicit Quadrilateral Shell Element

The present study introduces a 4-node quadrilateral shell element (which is called EQ7) for the analysis of plates and shells. The element is a flat element with 6 degrees of freedom at each node; three displacements and three rotations. It is based on the Explicit Finite Element Method. All quantities, matrices, etc., are explicitly derived. We apply to the shell element a number of modes and besides the Modal Stiffness Matrix we introduce the Modal Mass Matrix and the Modal Geometric Matrix. We employ also an iterative scheme for the solution of the linear system of equations. Numerical simulations are provided. Stress Wave Patterns are found in deforming plates and shells. Because all quantities are explicitly derived, the theory and method is suited for efficient computer implementation.

Vibration and damping analysis of functionally graded carbon nanotubes reinforced hybrid composite shell structures

The present article deals with the vibration and damping analysis of functionally graded carbon nanotubes reinforced hybrid composite (FG-CNTRHC) shell structure which consists of conventional carbon fiber as reinforcing phase and single-walled carbon nanotubes based polymer as matrix phase. The Eshelby–Mori–Tanaka approach in conjunction with strength of material approach is implemented to obtain the material properties of FG-CNTRHC structures. The material properties of FG-CNTRHCs are assumed to be graded through the thickness direction according to power law distributions of the volume fraction of carbon fibers and fiber orientations. An eight node shell element considering transverse shear effect according to Mindlin’s hypothesis has been formulated for finite element modelling and analysis of such functionally graded hybrid composite shell structures. The formulation of shell midsurface in an arbitrary curvilinear coordinate system based on the tensorial notation also presented. The Rayleigh damping model has been implemented in order to study the effects of carbon nanotubes (CNTs) on damping capacity of such hybrid shell structures. Different types of spherical shell panels have been analyzed in order to study the time and frequency responses. The influences of CNTs, carbon fiber, geometry of the shell, power law index and material distributions on the vibration damping characteristics of FG-CNTRHC shell structures have also been presented and discussed. Various types of FG-CNTRHC shell structures (such as spherical, ellipsoidal, doubly curved and cylindrical) have been analyzed and discussed in order to comparative studies in terms of settling time, first resonant frequency and absolute amplitude corresponding to first resonant frequency and the effects of CNTs on vibrations responses of such shell structures are also presented.

An accurate [formula omitted] finite element model of moderately thick and deep laminated doubly curved shell considering cross sectional warping

A C0 finite element model based on the higher order shear deformation theory has been developed for moderately thick and deep doubly curved laminated composite shells of various shapes. The new accurate equations of elastic deformation by incorporating cross sectional warping of the laminated shells have been developed. The present finite element model has been developed by using eight noded isoparametric shell element with nine degrees of freedom per node. The numerical analysis of laminated shells using the present model has been carried out under sinusoidal loading. The present formulation has been validated by comparing the results in terms of deflection and stresses for moderately thick and deep shells with those obtained from the three dimensional elasticity solution.

Geometrically nonlinear static FE-simulation of multilayered magneto-electro-elastic composite structures

A fully geometrically nonlinear finite rotation shell element for static analysis of layered magneto-electro-elastic (MEE) coupled composite structures is proposed. Reissner–Mindlin first-order shear deformation (FOSD) theory with full geometrically nonlinear strain–displacement relations and finite rotations is used to obtain the variational formulation. The scalar electric and magnetic fields are assumed along with the quasi-static behavior of MEE layers. Electric and magnetic potentials are assumed to vary quadratically in the transverse direction. Three linear constitutive relations are used describe the magneto-electro-elastic coupling. The magneto-electro-elastic composite four node shell element behavior is refined by embodying an assumed natural strain (ANS) method for transverse shear strains, and an enhanced assumed strain (EAS) method for in-plane bending strains. The developed finite element model is deployed for static analysis of layered MEE structures in sensor and actuator configurations, and results are compared with the available references. Additionally, several numerical examples are simulated to show the potentiality and predictive capabilities of the proposed finite element method.

A rectangular shell element formulation with a new multi-resolution analysis

A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape functions. The basic node shape functions are constructed from shifting to other three quadrants around a specific node of a basic element in one quadrant and joining the corresponding node shape functions of four elements at the specific node. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. The node shape functions of Kronecker delta property make the treatment of element boundary condition quite convenient and enable the stiffness matrix and the loading column vectors of the proposed element to be automatically acquired through quadraturing around nodes in RL adjusting. As a result, the traditional 4-node rectangular shell element is a mono-resolution one and also a special case of the proposed element. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The simplicity and clarity of node shape function formulation with the Kronecker delta property, and the rational MRA enable the proposed element method to be implemented more rationally, easily and efficiently than the conventional mono-resolution rectangular shell element method or other corresponding MRA methods.

패치 로딩을 받는 알루미늄 합금 A6082-T6 사각형 판의 임계 탄성좌굴하중 검토

In this paper, we examined the problem of the structural stability according to the patch load of a rectangular plate that reflects the material properties of A6082-T6 is used primarily for marine plant structure. it applied to the four patch loading shapes, the effect of aspect ratio, a boundary condition and calculated the critical elastic buckling load. Calculating the critical elastic buckling load, During the eigenvalue buckling analysis it is applied to the shell181 as 4 node shell element. when the plate subjected to patch loading compare to the plate under a uniform axial compression load, it is possible observed to occur the different elastic buckling behaviour and it could be confirmed that it is affected significantly on a variable position and type of loadings, such as the effect of the aspect ratio. Also, Critical elastic buckling load according to th patch loading type in simply supported rectangular plate ,  are calculated 67%(Loading type I), 119 %(Loading type II), 76 %(Loading type III), 160 %(Loading type IV), respectively. Loading type I and III could be determined with the strong elastic buckling behavior much more than Loading type II and IV.

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The flat shell element is constructed by combining a quadrilateral area coordinate method (QAC) based membrane element AGQ6-II, and a Timoshenko beam function (TBF) method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory (FSDT), for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical results show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.

The MITC3 shell finite element enriched by interpolation covers

In this paper, we develop a scheme to enrich the 3-node triangular MITC shell finite element by interpolation cover functions. The MITC method is used for the standard and enriched displacement interpolations. The enriched 3-node shell finite element not only captures higher gradients but also decreases inter-elemental stress jumps. In particular, the enrichment scheme increases the solution accuracy without any traditional local mesh refinement. Convergence studies considering a fully clamped square plate problem, cylindrical shell problems, and hyperboloid shell problems demonstrate the good predictive capability of the enriched MITC3 shell finite element, even when distorted meshes are used. We evaluate the effectiveness of the method, and also illustrate the use of the enrichment scheme applied only locally through the solution of two additional shell problems: a shaft–shaft interaction problem and a monster shell problem.