A layer-wise triangle for analysis of laminated composite plates and shells

The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation is chosen for the normal displacement. A substructuring technique is used to eliminate the in-plane degrees of freedom during the assembly process thus reducing substantially the computationed costs. The element performance is evaluated in the static and dynamic analysis of different laminate plate and shell structures.     

Maximization of buckling load of laminated composite plates with central circular holes using MFD method

This paper addresses optimal design of simply supported symmetrically laminated composite plates with central circular holes. The design objective is the maximization of the buckling load, and the design variable is considered as the fiber orientation. The first-order shear deformation theory is used for the finite element analysis. The study is complicated because the effects of bending–twisting coupling are also included for the buckling optimization. The modified feasible direction method is used to solve the optimization problems. Finally, the effect of different number of layers, boundary conditions, width-to-thickness ratio, plate aspect ratios, hole daimeter-to-width ratio, and load ratios on the results is investigated.     

复合材料悬臂外伸板的非线性动力学建模及数值研究

研究了横向气动载荷和参数激励联合作用下复合材料悬臂外伸矩形板在伸出过程中的非线性动力学问题.根据Reddy的高阶剪切层合板理论,应用Hamilton原理建立了外伸板在横向气动力和参数激励作用下的非线性动力学方程,其中横向气动力采用一阶活塞气动力.然后应用Galerkin方法对系统偏微分形式的非线性方程进行离散,得到了一组时变系数的非线性动力学方程.在此方程的基础上,对复合材料悬臂外伸板进行了数值模拟分析,讨论了外伸速度对悬臂外伸板非线性动力学特性的影响.     

A split least-squares characteristic mixed finite element method for Sobolev equations with convection term

In this paper, a split least-squares characteristic mixed finite element method for a kind of Sobolev equation with convection term is proposed, in which the characteristic method is based on the approximation of the material derivative term, that is, the time derivative term plus the convection term. The resulting least-squares procedure can be split into two independent symmetric positive definite sub-schemes and does not need to solve a coupled system of equations. Theory analysis shows that the method yields the approximate solutions with optimal accuracy in L²(Ω) norm for the primal unknown and in H(div;Ω) norm for the unknown flux, respectively. Numerical examples in one dimension, which are consistent with the theoretical results, are provided to demonstrate the characteristic behavior of this approach.     

基于APDL的夹层玻璃面板非线性有限元分析

为使夹层玻璃面板的计算能够更符合实际受力特点,基于ANSYS的APDL,运用参数化建模、参数化施加载荷与求解以及参数化后处理显示的手段,考虑大位移非线性效应,实现夹层玻璃面板仿真分析．在有限元分析中,结合夹层玻璃面板常见的4边支撑形式,既考虑玻璃面板膜面应力对夹层玻璃承载力的非线性影响,又考虑目前《玻璃幕墙工程技术规范》（以下简称《规范》）中所没有考虑的中间层聚乙烯醇缩丁醛Polyvinyl Butyral（PVB）胶片对夹层玻璃承载力的影响,并与《规范》进行对比分析．在对大量不同规格夹层玻璃面板的有限元分析结果的基础上,对《规范》中关于夹层玻璃在静力载荷作用下的计算公式进行修正,给出修正因数,使其符合实际受力特点．该结果可为幕墙设计提供参考．     

A mortar spectral method for the analysis and optimization of L-shaped laminated plates

We present a new mortar approach in the spectral context for the analysis and optimization of L-shaped thin composite laminates. Its roots may be found in the (very few) existing mortar approaches for the bi-Laplacian that are herein extended to handle the fourth-order elliptic operator governing thin anisotropic laminates. For the computation of the structural matrices, exact symbolic integration is used rather than more classical Gauss–Lobatto quadrature schemes. Thanks to the underlying spectral approach, considerable CPU times savings are obtained compared with finite-element approaches when the optimal design of the laminates is pursued. A few numerical studies that are concerned with the analysis and the optimization of L-shaped single-layered plates are described in detail.     

A mixed shear flexible finite element for the analysis of laminated plates

A mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated. The element consists of three displacements, two rotations, and three moments as the generalized degrees of freedom per node. The numerical convergence and accuracy characteristics of the element are investigated by comparing the finite element solutions with the exact solutions. The present study shows that reduced-order integration of the stiffness coefficients due to shear is necessary to obtain accurate results for thin plates.     

层合板固有频率分析的B样条小波元法

结合弹性材料修正后的H—R变分原理和区间B样条小波函数,建立Hamilton正则方程的区间B样条小波元列式．首先简要地介绍了弹性材料修正后的H—R变分原理,然后将区间B样条小波的尺度函数作为基函数,详细地推导了Hamilton正则方程的区间B样条小波元列式．数值算例验证了B样条小波元列式的正确性．     

Large scale micro finite element analysis of 3D bone poroelasticity

In this paper, a solver for poroelasticity problems related to osteoporotic human bones is discussed. Osteoporosis is a major health problem that compromises the integrity of bones. A good understanding of the disease requires an accurate simulation of the physics. For that purpose, a finite element solver based on Biot’s consolidation equations has been developed. A mixed formulation is used to discretize the geometries taken from medical imaging. The resulting indefinite linear systems are solved by Krylov space methods supplemented by variants of Schur complement-based block preconditioners.     

Effects of random system properties on the thermal buckling analysis of laminated composite plates

This paper examines the effect of random system properties on thermal buckling load of laminated composite plates under uniform temperature rise having temperature dependent properties using HSDT. The system properties such as material properties, thermal expansion coefficients and thickness of the laminate are modeled as independent random variables. A C⁰ finite element is used for deriving the eigenvalue problem. A Taylor series based first-order perturbation technique is used to handle the randomness in the system properties. Second-order statistics of the thermal buckling load are obtained. The results are validated with those available in the literature and Monte Carlo simulation.     

A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates

In view of the increasing interest in using composite materials for aerospace structures, the analysis of laminated composite plates becomes essential. A three-dimensional eight-node hybrid stress finite element method is developed for the analysis of laminated plates. The hybrid stress model is based on the modified complementary energy principle and takes into account the transverse shear deformation effects. The displacement field is interpolated through shape functions and nodal displacements. All three displacement components are assumed to vary linearly through the thickness of each lamina. The stress field is interpolated through assumed stress polynomials with 55 stress parameters for each lamina. All six stresses are included and satisfy the homogeneous equilibrium equations. The validity of the hybrid stress finite element model is determined by comparing the predicted numerical results with the existing three-dimensional elasticity solutions. Excellent accuracy and fast convergence are observed in the numerical results.     

Recent developments in the Trefftz method for finite element and boundary element applications

In 1926 E. Trefftz published a paper about a variational formulation which utilizes boundary integrals. Almost half a century later researchers became interested again in the ideas of Trefftz when the potential advantage of the Trefftz-method for an efficient use in numerical application on a computer was recognized. The concept of Trefftz can be used both for finite element and boundary element applications. A crucial ingredient of the Trefftz- method is a set of linearly independent trial functions which a priori satisfy the governing differential equations under consideration. In this paper an overview of some recent developments to construct trial functions for the Trefftz-method in a systematic manner is given. Using different types of approximation functions (singular or non-singular) we can obtain very accurate finite element and boundary element algorithms.     

Accuracy estimation in the finite element analysis of transverse bending of thin flat plates

As a basic study for the establishment of an accuracy estimation method in the finite element method, this paper deals with the problems of transverse bending of thin, flat plates. From the numerical experiments for uniform mesh division, the following relation was deduced, ε ∝ (h/a)^k, k 1, where ε is the error of the computed value by the finite element method relative to the exact solution and h/a is the dimensionless mesh size. Using this relation, an accuracy estimation method, which was based on the adaptive determination of local mesh sizes from two preceding analyses by uniform mesh division, was presented.

A computer program using this accuracy estimation method was developed and applied to 28 problems with various shapes and loading conditions. The usefulness of this accuracy estimation method was illustrated by these application results.     

Nonconforming finite element approximation of the Giesekus model for polymer flows

We present a numerical approximation of the Giesekus equation which is considered as a realistic model for polymer flows. We use nonconforming finite elements on quadrilateral grids which necessitate the addition of two stabilization terms. An appropriate upwind scheme is employed for the convective term. The underlying discrete Stokes problem is then analysed. Finally, numerical tests are presented in order to validate the code, illustrating its good behavior for large Weissenberg numbers. Comparisons with Polyflow® and with the literature are also carried out.     

A class of C finite elements for the static and dynamic analysis of laminated plates

A general higher-order deformation theory is developed to analyse the behaviour of an arbitrary laminated fibre-reinforced composite plate. Three-dimensional effects such as the warping of sections and the presence of interlaminar stress field components are taken into account assuming a power series expansion of displacements along the thickness. A class of C⁰ finite element models based on this theory is then developed for mono- and bi-dimensional elements. Applications of the models to bending and vibration of laminated plates are then discussed. The present solutions are compared with those obtained using the three-dimensional elasticity theory, classical laminate theory and other higher-order theories.     

组合结构等效阻尼比的确定及在有限元计算中的应用

针对组合结构动力响应计算中,一般根据工程经验确定结构阻尼比,往往导致结构动力响应计算结果偏小,不利于结构安全评估的问题,首先根据复阻尼理论与结构动力学方法,推导出组合结构的等效阻尼比计算公式;然后,以某体育场组合结构为工程背景,在有限元法基础上使用ANSYS软件建立该结构的有限元模型.根据计算出的自振特性以及利用ANSYS二次开发功能所形成的阻尼刚度矩阵,实现等效阻尼比的有限元法求解.计算结果表明,等效阻尼比能够正确反映组合结构的动力特性,从而可以科学地计算其动态响应.     

An efficient facet shell element for corotational nonlinear analysis of thin and moderately thick laminated composite structures

In the present work, an efficient facet shell element for the geometrically nonlinear analysis of laminated composite structures using the corotational approach is developed. The facet element is developed by combining the discrete Kirchhoff-Mindlin triangular bending element (DKMT), and the optimal membrane triangular element (OPT). The membrane-bending coupling effect of composite laminates is incorporated in the formulation, and inconsistent stress stiffness matrix is formulated. Using corotational formulation and the proposed facet element, some example laminated composite structures with geometric nonlinearity are analyzed, and the results are compared with those found using other facet elements.