8-node Serendipity Research Articles

Buckling analysis of functionally graded materials by dynamic approach

Laminated composites exhibit difference in the mechanical properties at the interface between two materials resulting in stress concentration. This may lead to damages in the form of delamination, matrix cracking and adhesive bond separation. Functionally Graded Materials (FGM) are formed by gradual variation of two or more material over a particular volume, thereby overcomes these issues. Buckling problems of FGM plates are usually solved by static approach. In some cases, particularly non-uniform loading and geometric discontinuity, the stress concentration usually occurs. In such cases, the solution to the buckling problem by dynamic approach is most suitable. In the dynamic approach, the natural frequencies are calculated by applying in-plane loads. As the intensity of the in-plane load increases, the frequency of the material decreases and finally becomes zero at the onset of buckling. The load at which the natural frequency becomes zero that load is called a buckling load. In this investigation, the vibration and buckling characteristics of FGM panels subjected to uniaxial and biaxial loading conditions have been studied by using the finite element method (F.E.M). In the Finite element (FE) formulation, the effective material properties of FGM plates are assumed to vary in the thickness direction according to the power-law distribution of volume fraction of the constituents. The plate is modelled by using 8-noded serendipity element by incorporating the effect of transverse shear deformation and rotary inertia. The effect of different parameters such as volume fraction index (n), the thickness of the panel (h) and boundary condition of the plate are considered to study the buckling behaviour of the FGM plate under uniaxial loading conditions.

A novel triangular boundary crack front element for 3D crack problems based on 8-node serendipity element

This paper developed a novel 6-node triangular boundary crack front element for 3D crack problems. The developed element method was constructed based on an 8-node serendipity element and a distance function that defines the distance from arbitrary point inside the element to the crack front. The specially constructed shape function captures the square-root asymptotic behavior of the distribution of the displacement nearby the crack front. In order to employ the crack front element in the dual boundary element method, conversion from conforming triangular crack front elements to non-conforming triangular ones was performed through a matrix transformation. In the implementation of dual boundary element method, a displacement extrapolation method is adopted to compute the stress intensity factor at the crack front. Finally, three examples were presented to verify the efficiency of our proposed crack front element. In all the numerical examples, the presented crack front element exhibits high accuracy and efficiency in the examples.

FE simulation of cylindrical RC containment structures under reserved cyclic loading

The nuclear containment structure is one of the most important infrastructure systems ensuring the safety of a nuclear power plant. The structural behavior of a cylindrical containment structure made of reinforced concrete (RC) with large dimensions and numerous rebars is complex and difficult to predict. The complex behavior of the RC containment structure has been investigated in an international collaboration project between the National Center for Research on Earthquake Engineering (NCREE) in Taipei, Taiwan and the University of Houston (UH), Houston, Texas. At NCREE two 1/13 scaled cylindrical RC containment specimens were tested under reversed cyclic loads [1]. At UH, a finite element simulation of the two tested specimens was developed using a finite element analysis (FEA) program SCS [2]. In the program, a new shell element, the so-called CSMM-based shell element, was developed based on the Cyclic Softened Membrane Model [3] and the formulation of an 8-node Serendipity curved shell element [4] with a multi-layer approach [5]. The UH simulated seismic behavior was close to the NCREE experimental results. This paper presents the theoretical development of the FEA program SCS and the comparisons of its predictions with the experimental structural behavior of the two RC containment specimens. This simulation model and the FEA program are excellent tools to develop effective performance-based design provisions.

English

English

A rigorous and unified mass lumping scheme for higher-order elements

In dynamic analysis with explicit time integration schemes, a lumped mass matrix (LMM) is preferable, because LMM can avoid solving the large scale simultaneous algebraic equations. Mathematically rigorous mass lumping schemes, such as the mass lumping by nodal quadrature and the row-sum technique, are applicable to only linear or bilinear elements. For higher-order elements, such as 8-node serendipity elements, the diagonal scaling procedure is the only lumping method that can be recommended to generate positive definite diagonal element mass matrices. Unfortunately, there is no mathematical theory in support of this approach. This study proposes a general mass lumping scheme applicable to higher order elements, where the virtual work of initial force is integrated over the problem domain that is viewed as the manifold covered by the finite element patches. By a series of numerical experiments, both free and forced vibration problems, it is suggested that even in the implicit time integration scheme the consistent mass matrix (CMM) can be superseded by the proposed LMM. Furthermore, the proposed LMM has much stronger adaptability to distorted meshes.

Vibration Analysis of Thick Arbitrarily Laminated Plates of Various Shapes and Edge Conditions

Free vibration analysis of arbitrarily laminated plates of quad, penta and hexagonal shapes, which have combinations of clamped, simply supported and free edge conditions is performed. The finite element formulation is based on first and higher order shear deformation theories to study the free vibration response of thick laminated composite plates. A finite element code is developed incorporating shear deformation theories using an 8-noded serendipity element. The effect of plate shape, arbitrary lamination and different edge conditions on natural frequencies and mode shapes are investigated. A systematic study is carried out to determine the influence of material orthotropy and aspect ratio on free vibration response. For various cases, the comparisons of results from present study showed good agreement with those published in the literature.

New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method

A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

Nonlinear modeling of composite plates with piezoceramic layers using finite element analysis

A finite element formulation for the vibration of piezoceramic laminated plates that takes hysteretic behavior into account is presented. Structural deformations of the layers are modeled using Mindlin plate theory where electro-mechanical coupling equations are formulated based on the same theory. Electro-mechanical coupling terms model orthotropic piezoelectric properties ( g 31≠ g 32), in addition to an orthotropic formulation for the mechanical properties of each plate layer. Lateral and transversal displacement fields are modeled with 8-node serendipity quadratic elements. Hysteretic behavior within the dielectric domain is implemented and simulated via the finite element method using an Ishlinskii model. Experimental hysteresis characterization for a single piezo layer and simulation results are presented. A coupled composite plate model is also tested under different loading conditions experimentally and numerically.

탄성지지된 집중질량을 갖는 변단면 후판의 진동해석

This study is undertaken for the vibration analysis of tapered thick plate with concentrated mass on elastic foundation. The boundary condition of the plate is analyzed with the 4-sides simply supported and 4-fixed basis. This study find out the frequency following the change in size for each foundational variable on Pasternak foundation, one of the two-parameter elastic foundation parameter that considered the shear layer to the Winkler foundation parameter. The concentrated mass is applied with the consideration of mass of the entire plate, and the change of frequency is studies on each location with the consideration of reacting for the three locations for concentrated mass. And, in order to find out the change of frequency on the thickness of the plate, it considered tapered ratio that linearly changes depending on the length of the plate with the thickness of the plate in x-direction, and the tapered ratio has changes with 4 types (<TEX>$\alpha$</TEX>=0.25, 0, 5, 0.75, and 1.0). For the interpretation, the program using finite element method (F.E.M.) is used and the element coordination is used the 8-node serendipity element. Therefore, the purpose of this study is to find out the characteristics of plate vibration under the mechanica vibration or external vibration factor to facilitate as the basic data of the design to secure the stability.

Stability and accuracy of finite element methods for flow acoustics. II: Two‐dimensional effects

AbstractThis is the second of two articles that focus on the dispersion properties of finite element models for acoustic propagation on mean flows. We consider finite element methods based on linear potential theory in which the acoustic disturbance is modelled by the convected Helmholtz equation, and also those based on a mixed Galbrun formulation in which acoustic pressure and Lagrangian displacement are used as discrete variables. The current paper focuses on the effects of numerical anisotropy which are associated with the orientation of the propagating wave to the mean flow and to the grid axes. Conditions which produce aliasing error in the Helmholtz formulation are of particular interest. The 9‐noded Lagrangian element is shown to be superior to the more commonly used 8‐noded serendipity element. In the case of the Galbrun elements, the current analysis indicates that isotropic meshes generally reduce numerical error of triangular elements and that higher order mixed quadrilaterals are generally less effective than an equivalent mesh of lower order triangles. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Study on the degeneration of quadrilateral element to triangular element

AbstractIn this paper, the problems involved in the process of degeneration of quadrilateral element into triangular element are thoroughly analysed. The contents include the formulation of the geometry mapping induced by collapsing one side of the quadrilateral element and the construction of the shape functions. The study focuses first on a 4‐node bilinear quadrilateral (Q4) element to 3‐node constant strain triangular (CST) element, and then on a 8‐node serendipity (Q8) element to 6‐node triangular element (T6). In the analysis, the quadrilateral element and degenerate triangular element are assumed to be enclosed by straight edges. The theoretical results show that there is another better approach to realize the degeneration, and that even for conventional approach of degeneration we can give more reasonable explanation to the unclear problems like the CST property in degenerate CST element and the necessity of the additional terms in degenerate T6 element. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Interpolation error estimates of a modified 8-node serendipity finite element

Interpolation error estimates for a modified 8-node serendipity finite element are derived in both regular and degenerate cases, the latter of which includes the case when the element is of triangular shape. For \(u \in W^{3, p}(K)\) defined over a quadrilateral K, the error for the interpolant \(\Pi_K u\) is estimated as \(|u-\Pi_K u|_{W^{\alpha, p}(K)}\le Ch^{3-\alpha}_K|u|_{W^{3,p}(K)}\) \((\alpha=0, 1)\), where \(1 \le p \le +\infty\) in the regular case and \(1\le p < 3\) in the degenerate case, respectively. Thus, the obtained error estimate in the degenerate case is of the same quality as in the regular case at least for \(1\le p<3\). Results for some related elements are also given.

Modification of the 8-node serendipity element

This paper presents modification of the 8-node serendipity quadrilateral element which is widely used in finite element analysis. First we give basic principle of constructing 8-D spaces including the Cartesian quadratic polynomial space when the quadrilateral is of bilinear isoparametric shape. Then we derive a concrete example of such a space, in which the isoparametric quadratic space is included as well. Explicit expressions of shape functions are given for the sake of practical use. It is also shown that the usual 6-node quadratic triangle is obtained by applying the node degeneration technique to the present element. Comments are also given on the isoparametric use of the present element and on some existing elements related to ours. Moreover, numerical results are included to show the effectiveness of our modification.

A new heterosis plate element for geometrically non-linear finite element analysis of laminated plates

In this study, a new nine-node quadrilateral, shear-deformable heterosis element is developed. In order to model this element, Kirchhoff constraints are modified using Reissner-Mindlin theory assumptions. All of the modifications are performed for first-order shear-deformation theory (FSDT). This new heterosis element is developed by modifying 8-node serendipity and twelve-node cubic polynomials. The new heterosis element is used with nine-node Lagrangian elements in finite element analysis of composite plates. A modified element is used in finite element analysis of linear and non-linear analysis considering the advantages of free of ‘shear locking’. Numerical results are presented by comparing Navier's series solution.

Field-consistency analysis of 27-noded hexahedral elements for constrained media elasticity

Most 3-dimensional stress analysis is currently performed using the 8-noded linear and the 20-noded quadratic (serendipity) hexahedral elements. Recent experience with the quadratic plate/shell elements show that the 9-noded Lagrangian elements are superior to the 8-noded serendipity elements in applications to thin plate/shell flexure. Extension of this logic suggests that a 27-noded Lagrangian hexahedral element formulation with field-consistency corrections is needed for robust and reliable 3-D modelling of constrained media problems. In this paper we examine the field-consistency aspects involved in the formulation of such an element.

Transient dynamics of composite sandwich plates using 4-, 8-, 9-noded isoparametric quadrilateral elements

A finite element method based on Mindlin's theory is employed in the prediction of the dynamic transient response of multilayered composite sandwich plates. Numerical convergence and stability of 4-noded linear, 8-noded serendipity, and 9-noded Lagrangian elements are established using an explicit time integration technique. A special mass matrix diagonalization scheme is adopted which conserves the total mass of the element and includes the effects due to rotary inertia terms. The parametric effects of the time step, finite element mesh, lamination scheme, and orthotropy on the transient response are investigated. Numerical results for deflections and stresses are presented under various boundary conditions and loadings. The results presented herein should be of interest to composite-structure designers, experimentalists, and numerical analysists in verifying their results.

Finite element analysis of reinforced and prestressed concrete structures including thermal loading

This paper describes the application of finite element techniques to the solution of nonlinear concrete problems. Reinforced concrete thick plates and shells are first considered for which both a perfect and strain-hardening plasticity approach are employed to model the compressive behaviour. A dual criterion for yielding and crushing in terms of stresses and strains is considered, which is complemented with a tension cut-off representation. Degenerate thick shell elements employing a layered discretisation through the thickness are adopted and both reduced and selectively integrated 8-node serendipity and heterosis elements are considered. Thermal loading of prestressed concrete structures is also considered which necessitates the inclusion of time effects in the analysis. The technique described in this paper involves concurrently solving an uncoupled set of equations within a time interval to provide both the displacement and temperature increments. A two-level time stepping scheme is employed to predict temperature changes within a time interval and elasto-viscoplastic material analysis is performed using an explicit forward-difference scheme incorporating an equilibrium iteration procedure. The constitutive model for the concrete is essentially identical to that employed for the plate and shell analysis. Numerical examples are presented for both types of analysis and comparison is made with experimental results whenever possible. Additionally, results for thermal loading are presented which indicate that a full transient thermal-mechanical analysis is sometimes essential in order to obtain a realistic structural response.

A hybrid-stress quadratic serendipity displacement mindlin plate bending element

A hybrid-stress plate bending element is developed for thin and moderately thick plates based on a Serendipity-type quadratic displacement assumption. The through-thickness displacement behavior is consistent with Mindlin plate theory, and all components of stress are included. By proper choice of the transverse shear stress distributions, the element stiffness possesses correct rank, and results show no signs of locking in the thin plate limit; these and other considerations discussed herein suggest that the stress assumption used is optimum for the 8-node element. Results are compared with 8-node Serendipity and 9-node Lagrange assumed-displacement elements. The present element demonstrates high accuracy for all problems considered and has no apparent deficiencies.

The “heterosis” finite element for plate bending

A new. high-accuracy, finite element for thick and thin plate bending is developed, based upon Mindlin plate theory. The element is a 9-node quadrilateral, which exhibits improved characteristics in comparison with the 8-node serendipity, or the 9-node Lagrange elements. In particular, the element stiffness possesses correct rank, and high accuracy is attainable for extremely thin plates. Due to the consistently good performance of the element, it is proposed as a candidate for inclusion in finite element programs available to the general user.