Enrichment of linear hexahedral finite elements using rotations of a virtual space fiber

The present paper deals with the enrichment of 3D low‐order finite elements. The used concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. A consistent stiffness matrix is obtained, allowing a better approximation of the actual solution compared with that resulting from low‐order finite elements. Implemented for two eight‐node hexahedral elements, the performance of the space fiber rotation concept is assessed by running some classical beam, plate, and shell benchmarks, and the obtained results are compared especially with those given by linear eight‐node and quadratic 20‐node hexahedral elements. In particular, it is shown that the developed elements accuracy is significantly superior to that of the classical eight‐node hexahedral element and close to that of the classical 20‐node hexahedral element. Copyright © 2013 John Wiley & Sons, Ltd.     

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

In this paper, we present a non‐linear finite element formulation for piezoelectric shell structures. Based on a mixed multi‐field variational formulation, an electro‐mechanical coupled shell element is developed considering geometrically and materially non‐linear behavior of ferroelectric ceramics. The mixed formulation includes the independent fields of displacements, electric potential, strains, electric field, stresses, and dielectric displacements. Besides the mechanical degrees of freedom, the shell counts only one electrical degree of freedom. This is the difference in the electric potential in the thickness direction of the shell. Incorporating non‐linear kinematic assumptions, structures with large deformations and stability problems can be analyzed. According to a Reissner–Mindlin theory, the shell element accounts for constant transversal shear strains. The formulation incorporates a three‐dimensional transversal isotropic material law, thus the kinematic in the thickness direction of the shell is considered. The normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and the resultant dielectric displacement fields. Accounting for material non‐linearities, the ferroelectric hysteresis phenomena are considered using the Preisach model. As a special aspect, the formulation includes temperature‐dependent effects and thus the change of the piezoelectric material parameters due to the temperature. This enables the element to describe temperature‐dependent hysteresis curves. Copyright © 2011 John Wiley & Sons, Ltd.     

A mixed hexahedral finite element to model the scattering of a deformed microstrip antenna

Microstrip antennas have a major interest in aeronautical applications due to their low profile. This paper deals with the impact of mechanical strain on the scattering properties of these antennas. Considering a weak coupling between electromagnetism and mechanical behavior, the same 3D hexahedral finite element discretization is used to solve both problems. A node-based approximation is used for mechanical displacement, while for the determination of the electromagnetic fields, a vector finite approximation is implemented to ensure a better consideration of electromagnetic boundary conditions. The weak electromagnetic formulation inducing integrals on open infinite domains, a Boundary Integral Method is used.     

A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method

This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to earlier approaches, we do not work with an interior penalty formulation as, e.g. for Nitsche techniques, but impose the constraints weakly in terms of Lagrange multipliers. Roughly speaking a stable and optimal discrete Lagrange multiplier space has to satisfy two criteria: a best approximation property and a uniform inf–sup condition. Owing to the fact that the interface does not match the edges of the mesh, the choice of a good discrete Lagrange multiplier space is not trivial. Here we propose a new algorithm for the local construction of the Lagrange multiplier space and show that a uniform inf–sup condition is satisfied. A counterexample is also presented, i.e. the inf–sup constant depends on the mesh‐size and degenerates as it tends to zero. Numerical results in two‐dimensional confirm the theoretical ones. Copyright © 2008 John Wiley & Sons, Ltd.     

A low‐order,hexahedral finite element for modelling shells

A thin, eight‐node, tri‐linear displacement, hexahedral finite element is the starting point for the derivation of a constant membrane stress resultant, constant bending stress resultant shell finite element. The derivation begins by introducing a Taylor series expansion for the stress distribution in the isoparametric co‐ordinates of the element. The effect of the Taylor series expansion for the stress distribution is to explicitly identify those strain modes of the element that are conjugate to the mean or average stress and the linear variation in stress. The constant membrane stress resultants are identified with the mean stress components, and the constant bending stress resultants are identified with the linear variation in stress through the thickness along with in‐plane linear variations of selected components of the transverse shear stress. Further, a plane‐stress constitutive assumption is introduced, and an explicit treatment of the finite element's thickness is introduced. A number of elastic simulations show the useful results that can be obtained (tip‐loaded twisted beam, point‐loaded hemisphere, point‐loaded sphere, tip‐loaded Raasch hook, and a beam bent into a ring). All of the gradient/divergence operators are evaluated in closed form providing unequivocal evaluations of membrane and bending strain rates along with the appropriate divergence calculations involving the membrane stress and bending stress resultants. The fact that a hexahedral shell finite element has two distinct surfaces aids sliding interface algorithms when a shell folds back on itself when subjected to large deformations. Published in 2004 by John Wiley & Sons, Ltd.     

Analysis of 3D problems using a new enhanced strain hexahedral element

The now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell finite elements, is here explored in a versatile 3D low‐order element which is identified as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near‐incompressibility to the analysis of locking‐prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non‐linear problems including finite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent stiffness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several finite strain tests. Some examples involve finite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples. Copyright © 2003 John Wiley & Sons, Ltd.     

基于流动坐标系的3维空间动力非线性有限元方法

为提高空间Timoshenko梁单元非线性问题的计算精度,在共旋坐标法的基础上,提出了一种改进的Timoshenko梁单元几何非线性分析方法。利用虚功原理得到改进空间梁单元的刚度矩阵;使用有限质点法中的逆向运动思路计算单元局部坐标系下的刚体旋转矩阵;根据整体坐标系与局部坐标系之间旋转角度的转化以及微分关系,求得空间梁单元的切线刚度矩阵;编制了相应的有限元程序,对多个经典的大变形结构进行几何非线性分析。计算结果印证了该文所提出改进方法的正确性,同时与传统共旋坐标法相比,具有更高的精度。     

A geometrically non‐linear piezoelectric solid shell element based on a mixed multi‐field variational formulation

This paper is concerned with a geometrically non‐linear solid shell element to analyse piezoelectric structures. The finite element formulation is based on a variational principle of the Hu–Washizu type and includes six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has eight nodes with four nodal degrees of freedoms, three displacements and the electric potential. A bilinear distribution through the thickness of the independent electric field is assumed to fulfill the electric charge conservation law in bending dominated situations exactly. The presented finite shell element is able to model arbitrary curved shell structures and incorporates a 3D‐material law. A geometrically non‐linear theory allows large deformations and includes stability problems. Linear and non‐linear numerical examples demonstrate the ability of the proposed model to analyse piezoelectric devices. Copyright © 2005 John Wiley & Sons, Ltd.     

A transition element for uniform strain hexahedral and tetrahedral finite elements

A transition element is presented for meshes containing uniform strain hexahedral and tetrahedral finite elements. It is shown that the volume of the standard uniform strain hexahedron is identical to that of a polyhedron with 14 vertices and 24 triangular faces. Based on this equivalence, a transition element is developed as a simple modification of the uniform strain hexahedron. The transition element makes use of a general method for hourglass control and satisfies first‐order patch tests. Example problems in linear elasticity are included to demonstrate the application of the element. Copyright © 1999 John Wiley & Sons, Ltd. This paper was produced under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.     

A new fast finite element method for dislocations based on interior discontinuities

A new technique for the modelling of multiple dislocations based on introducing interior discontinuities is presented. In contrast to existing methods, the superposition of infinite domain solutions is avoided; interior discontinuities are specified on the dislocation slip surfaces and the resulting boundary value problem is solved by a finite element method. The accuracy of the proposed method is verified and its efficiency for multi‐dislocation problems is illustrated. Bounded core energies are incorporated into the method through regularization of the discontinuities at their edges. Though the method is applied to edge dislocations here, its extension to other types of dislocations is straightforward. Copyright © 2006 John Wiley & Sons, Ltd.     

Thermal flutter analysis of large‐scale space structures based on finite element method

During the orbital day–night crossing period, the suddenly applied thermal loading is apt to introducing vibration on flexible appendages of large‐scale space structures. This kind of thermally‐induced vibration is a typical failure of modern spacecrafts. However, owing to the complexity of this problem, many earlier researches study only the vibration of simplified beam models, which can hardly describe the performance of practical structures. This paper aims at using the finite element method to analyse the non‐linear vibration of practical thin‐walled large‐scale space structures subjected to suddenly applied thermal loading. In this study, the coupling effect between structural deformations and the incident normal solar heat flux is considered; the necessary condition of thermally‐induced vibration is verified; and the criterion of thermal flutter is established. Copyright © 2006 John Wiley & Sons, Ltd.     

A hierarchic 3D finite element for laminated composites

In this paper a new 3D multilayer element is presented for analysis of thick‐walled laminated composites. This element uses two steps to calculate the full stress tensor. In the first step the in‐plane stresses are computed from the material law using a displacement approximation, and then the transverse stresses are calculated from the 3D equilibrium equations. Since the 3D equilibrium equations require high‐order interpolation functions, a hierarchic interpolation of displacements is used. The new element is compared with existing ones, e.g. from MSC.MARC. Copyright © 2004 John Wiley & Sons, Ltd.     

Thermal analysis of induction motors using 3D finite element method

Abstract

To design a reliable and economical induction motor, it is necessary to be able to predict accurately the temperature distribution within the motor. In this paper, a 3D thermal model of an induction motor is presented. Except for providing a more accurate representation of the problem, the proposed model can also reduce computer memory and time. The finite element method (FEM) is used to analyze the three dimensional (3D) heat flow equation which describes the thermal model. Galerkin's procedure is used to derive the element equations and first order tetrahedral elements are used to discretize the field region. Galerkin's time‐stepping scheme is employed to treat time differential terms. Values of surface heat transfer coefficients are obtained from the empirical formula and heat losses are revised by the factory test. Application of the proposed method to the analysis of a 9,000 HP induction motor yields temperature distribution very close to the experimental data.     

Multinode finite element based on boundary integral equations

A finite element constructed on the basis of boundary integral equations is proposed. This element has a flexible shape and arbitrary number of nodes. It also has good approximation properties. A procedure of constructing an element stiffness matrix is demonstrated first for one-dimensional case and then for two-dimensional steady-state heat conduction problem. Numerical examples demonstrate applicability and advantages of the method. © 1998 John Wiley & Sons, Ltd.     

弯张换能器的有限元设计

IV型弯张换能器是水声领域中一类低频、大功率换能器，其理论分析通常采用有限元法。利用ANSYS软件建立了800Hz的IV型弯张换能器的有限元模型，进行结构分析与设计。根据分析的结果制作出样机，测试的结果与理论分析基本符合。     

State space finite element analysis for piezoelectric laminated curved beam with variable curvature

ABSTRACT

A six-variable state vector formulation for static deformation of the laminated curved beam bonded with piezoelectric actuators is deduced. The 2D numerical solution for the piezoelectric laminated curved beams (PLCB) is explored. Then the distributions of the electrical and mechanical fields along the beam thickness direction are investigated analytically. The static shape control is researched for a laminated half circular beam covered with piezoelectric actuators. Comparisons with the available results show the reliability of the proposed method. At the end a spiral laminated piezoelectric structure is analyzed and the parameter study is carried out using the presented method.     

A finite element model of shape memory polymer composite beams for space applications

Structures made of shape memory polymer composite (SMPC), due to their ability to be formed into a desired compact loading shape and then transformed back to their original aperture by means of an applied stimulus, are an ideal solution to deployment problems of large and lightweight space structures. In the literature, there is a wide array of work on constitutive laws and qualitative analyses of SMP materials; dynamic equations and numerical solution methods for SMPC structures have rarely been addressed. In this work, a macroscopic model for the shape fixation and shape recovery processes of SMPC structures and a finite element formulation for relevant numerical solutions are developed. To demonstrate basic concepts, a cantilever SMPC beam is used in the presentation. In the development, a quasi‐static beam model that combines geometric nonlinearity in beam deflection with a temperature‐dependent constitutive law of SMP material is obtained, which is followed by derivation of the dynamic equations of the SMPC beam. Furthermore, several finite element models are devised for numerical solutions, which include both beam and shell elements. Finally, in numerical simulation, the quasi‐static SMPC beam model is used to show the physical behaviors of the SMPC beam in shape fixation and shape recovery. Copyright © 2015 John Wiley & Sons, Ltd.     

A semi‐analytical curved element for linear elasticity based on the scaled boundary finite element method

This work introduces a semi‐analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate that enlarges, shrinks, or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems, computations are performed in the frequency domain. Results of this work are validated using the global matrix method and standard finite element analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling of piezoelectric transformers using finite‐element technique

Abstract

In this work, the modeling of piezoelectric transformers using the finite‐element technique is presented. A 3‐D finite element method solver, which employs 20‐node brick‐element formulation, is developed. Using the solver, the characteristics of piezoelectric transformers under different operating frequencies can be simulated. Also, the solver is capable of accounting for the effects of the electrical loadings attached to the output electrodes of piezoelectric transformers. The modeling results for two different types of piezoelectric transformers, the Rosen‐modal‐type and the unipoled‐disk‐type, are presented. For the Rosen‐modal‐type devices, the simulated voltage gains and the phase differences are validated with our measured results. Also, the simulated results of the unipoled‐disk‐type transformers agree with the measured results found in previously published literature. The effects of electrical loadings on these piezoelectric transformers are also discussed.     

Smart element method II. An element based on the finite Eshelby tensor

In this study, we apply the newly derived finite Eshelby tensor in a variational multiscale formulation to construct a smart element through a more accurate homogenization procedure. The so‐called Neumann–Eshelby tensor for an inclusion in a finite domain is used in the fine scale feedback procedure to take into account the interactions among different scales and elements. Numerical experiments have been conducted to compare the performance and robustness of the new element to earlier formulations. The results showed that the smart element constructed via the Neumann–Eshelby tensor of a finite domain provides better numerical accuracy than that constructed via the Eshelby tensor of an infinite domain. Moreover, it can relieve volumetric locking. Copyright © 2005 John Wiley & Sons, Ltd.