广义康托洛维奇法解任意四边形板的弯曲问题

本文从变分原理和双线性坐标变换出发,采用基于三次B样条函数的广义康托洛维奇法得到了带有各种边界条件任意四边形板弯曲的近似解答。样条函数广义康托洛维奇法是一种数值型的康托洛维奇法,因而它既能化二维问题为一维同题,同时又具有样条函数法收敛快、精度高、处理边界条件方便等优点。推导出的计算格式适用于各种边界条件,使梯形板、平行四边形板和矩形板的弯曲问题为本文的特殊情况。本文方法与通常有限元法相比,具有计算量小、精度高等显著特点,且通用性强,是一种很有前途的计算方法。     

梯形断面曲杆的应力分析与起重吊钩的计算

本文给出了平面问题梯形断面曲杆的极坐标平衡微分方程,按照弹性理论,探讨了梯形断面曲杆一端受集中载荷作用的解,计算了此种截面的各种标准吊钩。本文的研究,既为非矩形断面曲杆提供了一种分析方法,又为梯形断面起重吊钩的设计计算,提供了更为合理的理论基础。     

梯形板的非线性动力分析

基于弹性板的几何非线性动力平衡方程,首先建立了一个坐标变换将梯形板域变换到正方形域,并将控制方程及其相应的边界条件变换到该正方形域内,然后通过引入中间变量将控制方程降阶,并利用问题的数学物理关系将边界条件进一步简化,在正方形域内对板的控制方程应用伽辽金法使问题变为时间域的非线性动力方程,最后应用参数摄动法得到了梯形板的几何非线性自由振动和动力响应,所得计算结果可供工程设计人员参考。     

低温泵降温时间的计算

本文继“低温泵降温时间的计算和１００００升／秒低温泵的抽气特性”［１］的一文后，通过数学处理，用梯形公式进行积分，最后给出降温时间的计算公式。简化了计算方法非易于掌握，可以作为低温泵工程设计的参考。     

任意四边形板的振动和稳定性分析

文献[1]导出了任意四边形板在简支边界条件下的一系列公式,本文在此基础上,进一步提出了在各种边界情况下诸如矩形、菱形、梯形等任意四边形板的振型函数的选取及自振频率的计算,同时也讨论了这类板的稳定性问题,分析了屈曲模式的选取和临界载荷的计算。本文的方法简便易行,且有通用性,对计算机内存要求小,特别适用在小型微机上推广应用。本文的计算公式只要稍加修正,就可推广于各向异性板的计算。文中把计算的各种固有频率和临界载荷的结果与解析法得到的结果进行了比较,均获得满意的结果。由此也表明了本文的方法是适宜和有效的。     

四边固支梯形板大挠度问题摄动解法

本文采用Voh—Karman薄板大挠度方程,以板中点挠度值作小参数求得了均布荷载下中面边界条件为Nn=o,Vs=o的固支梯形板的摄动解,本文特例与现有梯形板小挠度和矩形板大挠度结果比较吻合较好。文末还讨论了倾角对板挠度和内力的影响,所给图表对工程设计有实用价值     

样条函数双向迭代法分析薄板的振动特性

本文将康特洛维奇方法推广应用于板的几何非线性振动特性分析,也适用于线性振动特性分析。将振型函数展开为双向B 样条函数的级数,由哈密顿原理导出两组特征方程。这种方法大大地减少了所需要的计算机内存和计算时间,可在微机上进行运算。通过算例表明,该方法具有很高的计算速度和精度,可推广应用于非规则板和柱壳的线性及非线性振动特性分析。     

最小二乘配线法分析各向异性梯形板横向振动问题

本文通过一线性平面映射,将任意梯形域映射为一直角梯形域,并取幂级数和切比雪夫多项式为挠度基函数。采用最小二乘配线法成功地分析了各向异性梯形板的横向振动特性。     

刚性基底上弹性约束矩形板的屈曲行为分析

对刚性基底上非加载边弹性约束矩形板在固支边均匀面内压力作用下的屈曲行为进行了分析研究。用里兹能量变分法建立确定板屈曲强度的本征值问题,利用满足边界条件的屈曲位移函数导出板屈曲系数计算公式。将该方法用于矩形钢管混凝土钢板局部屈曲的分析和计算,提出了目标板边界约束系数计算公式。试验结果表明,方形钢管混凝土柱钢板局部屈曲强度计算值与试验值吻合良好,钢板边界弹性约束的处理和约束系数的计算方法是有效的。     

非规则梁桥的模态推倒分析

在模态推倒分析（MPA）基本概念的基础上,研究了MPA预计非规则梁桥的地震位移需求的具体细节。首先分析了桥梁位移参考点的选择位置、能力谱的形式、非弹性需求谱的构建以及位移组合方式等,然后分别采用MPA和非线性时程分析（ITHA）计算了4座非规则梁桥的横桥向地震位移需求,并比较了MPA与ITHA的计算结果。结果表明,桥墩屈服后,虽然非规则梁桥的各主要模态之间有不同程度的耦合,只要采用合理的MPA操作过程,仍能够得到合理的地震位移需求。     

扁壳有限条的静力和动力分析

本文用限条法导出了分析二次抛物形扁壳的计算模式。所采用的曲条单元可用于分析在某一方向曲率较大的二次抛物壳体。经过蜕化,它还可计算双曲扁壳、柱壳及析板等结构。用这一摸式在微型机上编制了FORTRAN静力和动力程序,并对各种正、负及零高斯曲率扁壳进行了计算。对双曲马鞍型壳还进行了静力和动力试验,将理论计算值与实验结果进行比较,两者符合较好。将有限条法的计算情况与有限元法进行比较,前者具有计算精度高、省时、省内存等优点,并使许多问题可在微型机上解决。     

Local Instability and Free Vibration of Supported Plates Using the Basic Plate Triangle

This paper extends the numerical method, originally developed by Onate and his colleagues for the static analysis of plates, to enable modal (vibration) and bifurcative (buckling) analyses of plates to be undertaken. The procedure uses a rotation-free triangular element, and is based on combining the finite element method and the finite volume method so as to produce a triangular element with only three displacement degrees of freedom. Elastic stiffness, stability (geometric stiffness) and mass matrices are developed using the mixed formulation, and these are implemented in routine computer coding in order to demonstrate the validity and efficacy of the solution technique when compared with results reported by independent investigators. Natural frequencies and local buckling coefficients are given for plates with interior line supports, and these are used to illustrate the prowess of the numerical technique for the analysis of a wide class of plate buckling and vibration problems, whose analysis by non-discretisation techniques has found favour recently in deference to general finite element modelling which tends to introduce some inaccuracies. The element developed in this paper, however, is both accurate and has the attractive meshing characteristics of the finite element method for analysing more arbitrary geometric structural topologies.     

A novel hybrid-Trefftz finite element for symmetric laminated composite plates

International Journal of Mechanics and Materials in Design - A novel hybrid-Trefftz finite element (HTFE) for the analysis of symmetric laminated composite plates has been developed. Unlike the...     

FE Stress Analysis of Thick Composite Laminates with a Hole in Bending

In this work, the stress analysis of isotropic and ortotropic laminae both with a hole and without a hole and laminated both with a hole and without a hole composite plates have been examined using the finite element method. In order to solve the problem, a computer program has been written by using characteristics of eight-node isoparametric plane element. The calculations have been tested on various composite and steel materials by this program. The results have been shown in diagrams and tables and compared with literature. It was observed that the stress distributions in the plate with a hole was totally different from the plate without a hole. The analyses have showed that, the elastic stresses have been gradually reduced as moving from the first layer to the second.     

A mixed 3D finite element for modelling thick plates

Based on the Hellinger-Reissner variational principle, we formulate a mixed 3-d finite element for plate bending. This element is used to model thick plates and alleviates the problem of shear-locking in plates with large length/thickness ratios. The computer code which was used here, is available.     

A novel smart hybrid-Trefftz finite element for smart laminated composite plates

A novel smart hybrid-Trefftz finite element ( HTFE ) has been developed for the analysis of smart laminated composite plates. The substrates of the smart plates are symmetric and antisymmetric cross-ply plates. The derivation of this HTFE is devoid of the complicated task of finding the particular solutions of simultaneous governing partial differential equations. The Trefftz functions are constructed from the finite number of free-field exact solutions of the homogeneous simultaneous governing partial differential equations of the element domain in a straightforward manner without transforming them into a single governing equation. The HTFE is validated with the exact solutions of the smart composite plates. It is observed that this HTFE is an efficient finite element and can be utilized for the analysis of active control of smart composite structures.     

Finite element analysis for geometrically nonlinear deformations of smart functionally graded plates using vertically reinforced 1-3 piezoelectric composite

In this paper, a finite element model has been developed for the geometrically nonlinear static analysis of simply supported functionally graded (FG) plates integrated with a patch of vertically reinforced 1-3 piezoelectric composite material acting as a distributed actuator. The material properties of the functionally graded substrate plate are assumed to be graded only in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. The analysis of the electro-elastic coupled problem includes the transverse deformations of the overall plate to utilize the transverse normal actuation by the distributed actuator for counteracting the nonlinear deformations of smart functionally graded plates. The nonlinear governing equations of equilibrium are solved by using direct iteration method with under-relaxation. The numerical illustrations suggest the potential use of the distributed actuator made of vertically reinforced 1-3 piezoelectric composite material for active control of nonlinear deformations of smart functionally graded plates. The effect of variation of piezoelectric fiber orientation in the distributed actuator on its control authority for counteracting the nonlinear deformations of smart functionally graded plates has also been investigated.     

Analysis of thermo-elastic plates based on Reissner’s mixed variational theorem

Analysis of composite/sandwich plates under thermal loads has greater significance due to its extensive application in ocean and aerospace structures. This paper addresses the analysis of composite/sandwich plates under thermal load using layer-wise mixed finite element method. The Reissner mixed variational theorem (RMVT) has been used for the thermal analysis of plates. Transverse stress assumptions are made in the framework of RMVT and the resulting finite element describes a priori inter-laminar continuous transverse shear and normal stresses. This method is equally applicable to the analysis of plates under mechanical and thermal loads. Numerical examples are solved to validate the present formulation using a code developed in C-language and the results obtained with the present model are in good agreement with the analytical solutions available in literature.     

Effective hybrid hierarchical element generator for vibration analysis of plates

Cost effective high precision hybrid elements are presented in a hierarchical form for vibration analysis of plates. The elements are constructed by introducing computer installed hierarchical element generator algorithms which take advantage of the exact analytical treatment of the energy integrals automatically. Additional benefits accrue from: (i) the careful selection of assumed stresses and displacements satisfying finite element requirements, and maintaining the correct stiffness rank and invariance; (ii) the ability to reduce computational costs associated with various operations and the independence with respect to element geometries, which serve to build up a methodology to handle the generation of finite elements in any general purpose finite element system efficiently. Extensive numerical studies are made to predict the natural frequencies and harmonic response of plates with different boundary conditions. Accuracy of the solutions is assessed by comparison with the well established results. The noteworthy aspects of the applications are that the proposed elements are faster than those cited previously, and show a more favourable comparison to the analytical solutions for a wider range of vibration modes by maintaining rapid convergence characteristics.     

Finite element analysis of laminated composite plates using zeroth-order shear deformation theory

In this paper a generalized finite element model is developed for static and dynamic analyses of laminated composite plates using zeroth-order shear deformation theory (ZSDT). The theory ensures the parabolic distribution of transverse shear stresses across the plate thickness. A four-noded plate element is considered in this model and the generalized nodal variables are expressed using Lagrangian linear interpolation functions and Hermitian cubic interpolation functions. The solutions of the finite element model have been compared with the existing solutions for symmetric and antisymmetric laminated composite plates. The comparison confirms that the ZSDT can be efficiently used for finite element analysis of both thin and thick plates with high accuracy.