Dynamic stability analysis of composite skew plates subjected to periodic in-plane load

Here, the dynamic stability characteristics of simply supported laminated composite skew plates subjected to a periodic in-plane load are investigated using the finite element approach. The formulation includes the effects of transverse shear deformation, in-plane and rotary inertia. The boundaries of the instability regions are obtained using the Bolotin's method and are represented in the non-dimensional load amplitude-excitation frequency plane. The principal and second instability regions are identified for different parameters such as skew angle, thickness-to-span ratio, fiber orientation and static in-plane load.     

Out-of-plane behaviour of partially composite or sandwich beams by exact and Finite Element Methods

The out-of-plane vibrations of composite beams with interlayer slip or three-layer sandwich beams are theoretically and numerically investigated in this paper for general boundary conditions. The governing dynamics equations are derived by applying the Hamilton's principle. A Finite Element Resolution is presented for general boundary conditions, and compared to the exact solution based on the resolution of a tenth-order differential equation. The Finite Element Method may exhibit slip locking phenomenon for very stiff connection, a phenomenon widely investigated in the past for the in-plane behaviour of partially composite beams or sandwich beams. This slip locking, analogous to the shear locking for Timoshenko beams, can be faced with some relevant interpolation shape functions of the same order for each kinematics variables, namely the deflections and the torsion angle. The numerical results are presented for layered wood beams and laminated glass beams, with particular emphasis on the rate of convergence of the natural frequencies with respect to the number of Finite Elements. It is theoretically and numerically shown that the elastic spectra of the symmetrical composite beam are composed of two independent spectrums. One spectrum is independent of the connection parameter and can be studied using the solution of the non-composite action, whereas the second spectrum can be obtained from the resolution of a third-order polynomial equation using the Cardano's method. We show the phenomenon of cut-on frequency for this out-of-plane problem, a phenomenon already noticed for the in-plane Timoshenko beam vibrations. The exact method associated to a 10 degrees-of-freedom shape function can be formally associated with the dynamics stiffness method. The numerical and the exact approaches lead to the same dimensionless spectra, up to four digits.     

索网穹顶静动力分析及施工模拟

索网穹顶系国内首次采用新型结构形式,体系较为复杂,静动力分析及施工过程动态模拟显得特别重要。基于非线性有限元分析方法,本文对结构主次索网的协同工作性能进行了分析,并对动力性能做了深入探讨。鉴于索网穹顶结构施工成型的难点,运用ANSYS软件跟踪模拟分析施工过程中结构的响应,对类似结构的工程施工设计具有一定的参考价值。     

A semi-analytical analysis of the elastic buckling of cracked thin plates under axial compression using actual non-uniform stress distribution

An improved hybrid semi-analytical method for calculating elastic buckling load of a thin plate with a central straight through-thickness crack subject to axial compression is proposed. In the study, the actual non-uniform in-plane stress distribution is firstly conducted by using Muskhelishvili's complex variable formulation in conjunction with boundary collocation method. A deflection shape function, satisfying not only the outer boundary conditions but also the inner boundary conditions of the crack edges, is obtained by using domain decomposition method. Finally the buckling load of a cracked plate using Raleigh–Ritz energy method is calculated based on the actual in-plane stress distribution and the reasonable deflection shape function obtained. The effects of crack length, plate's aspect ratio are studied for thin plates with different boundary conditions. Results obtained from the proposed method are in good agreement with the existing numerical results and experimental ones. It is finally shown that the proposed method, based on a correct non-uniform in-plane stress distribution, is more accurate than the few existing analytical methods based on a uniform in-plane stress distribution.     

Non-linear free and forced vibrations of piezoelectric laminated shells in thermal environments

This article is concerned with the non-linear free vibration and transient response of laminated composite cylindrical and spherical shells with piezoelectric layers in thermal environments. The theoretical formulations are based on the first-order shear deformation theory and the von Kármán-type non-linear kinematics. The analysis is carried out using the quadratic C ⁰ eight-noded isoparametric element. The governing non-linear equations are solved by using the direct iteration method for the eigenvalue problem for free vibration and the Newmark average acceleration method in time integration in conjunction with the modified Newton-Raphson iteration scheme for the transient analysis. The validity of the numerical model is demonstrated by comparing the present results with those available in the literature. The effects of temperature, voltage, curvature, thickness, number of layers and boundary conditions on the non-linear free vibration and transient response of piezoelectric laminated cylindrical and spherical shells are investigated.     

Solution to the problem of axisymmetric and asymmetric dynamic instability of three-layered annular plates

This paper presents the solution to the dynamic stability problem of three-layered, annular plate loaded by compressive stress increasing in time. The solution enables the evaluation of the critical, dynamic loads corresponding to the various modes of plate buckling. The symmetrical cross-section structure of plate is described by the classical theory of sandwich plate with the broken line hypothesis, the nonlinear Kármán’s plate equations and linear physical relations. The solution is based on Bubnov–Galerkin method and finite difference method. The values of critical dynamic loads have been calculated by means of the stability criterion presented by (Volmir (1972) [1]). The comparison of values of critical dynamic and static loads is presented, using the dynamic ratio. The obtained results have been compared with those obtained for plate model built by means of finite element method. The calculations were carried out using the ABAQS system. The dynamic response of plate models examined by two methods is consistent.     

Static and dynamic interactive buckling of isotropic thin-walled closed columns with variable thickness

The present paper deals with static and dynamic analysis of interactive buckling of thin-walled closed columns with variable thickness subjected to in-plane constant and/or pulse loading. This investigation is concerned with thin-walled structures with corners bevelled at the angle of 45° under axial compression. The plate model is adopted for the structures. The material, all plates are made of, is subject to Hooke's law. The structures are assumed to be simply supported at the ends. The differential equations of motion have been obtained from Hamilton's principle. In this paper the static solution has been obtained by Koiter's asymptotic method in the second-order approximation. The study is based on the numerical method of the transition matrix using Godunov's orthogonalization. The interaction of an overall mode with two local modes having the same wavelength has been considered (i.e. three-mode approach). The nonlinear equations of dynamic stability are solved with the Runge–Kutta method. The calculations are carried out for settled imperfections.     

复合地基的地震动力反应分析

在综合考虑土体双曲线本构模型、增量迭代非线性算法和动力分析中的等价线性化方法的基础上 ,对复合地基进行了地震作用下的动力反应分析。通过一算例指出 :复合地基可以有效地改善天然地基的土力学性能和动力反应特性 ,是符合实际工程需要的地基处理技术。     

回填EPS混合土的防滑悬臂式挡墙地震稳定性分析

以一种带防滑齿的"T"型悬臂式挡土墙为对象,采用振动台模型试验揭示了分别回填EPS混合土和天然南京细砂时的挡墙地震稳定性特征。分析并比较了墙–土体系的地震反应以及墙背动土压力分布,重点讨论了试验的防滑悬臂式挡墙位移模式以及回填土性质对墙背动土推力的影响。试验结果表明,回填EPS混合土时,填土地表加速度反应相对更小。回填土的动土推力对墙体转动位移的贡献随激励峰值的增大而增大;墙–土惯性相互作用效应与回填土的动力变形模式密切相关。两种回填料下的墙背动土压力分布形态具有显著差异;砂土–挡墙体系的动土推力与地表峰值加速度间趋向非线性关系,作用点接近2/3墙高。回填EPS混合土时两者更接近线性关系,且动土推力作用点接近1/3墙高。两种体系的动土推力作用点随地表峰值加速度增大均略有下移。基于试验结果与几种经典的解析方法预测结果比较,给出了EPS混合土柔性挡墙抗震分析的几点建议。     

Dynamic in-plane transversal normal stresses in the concrete face of CFRD

Severe earthquakes can induce damages to Concrete Face Rockfill Dams (CFRDs) such as concrete cracking and joint’s water stops distressing where high in-plane transversal normal stresses develop. Although these damages rarely jeopardize the dam safety, they cause large water reservoir leakages that hinder the dam functioning. This issue can be addressed using well know numerical methods; however, given the wide range of parameters involved, it would seem appropriate to develop a simple yet reliable procedure to get a close understanding how their interaction affects the CFRD’s overall behavior. Accordingly, once the physics of the problem is better understood one can proceed to perform a detailed design of the various components of the dam. To this end an easy-to-use procedure that accounts for the dam height effects, valley narrowness, valley slopes, width of concrete slabs and seismic excitation characteristics was developed. The procedure is the dynamic complement of a method recently developed to evaluate in-plane transversal normal stresses in the concrete face of CFRD’s due to dam reservoir filling [¹]. Using these two procedures in a sequential manner, it is possible to define the concrete slab in-plane normal stresses induced by the reservoir filling and the action of orthogonal horizontal seismic excitations acting at the same time upstream-downstream and cross river. Both procedures were developed from a data base generated using nonlinear static and dynamic three-dimensional numerical analyses on the same group of CFRD’s. Then, the results were interpreted with the Buckingham Pi theorem and various relationships were developed. In the above reference, the method to evaluate the concrete face in-plane transversal normal stresses caused by the first reservoir filling was reported. In this paper, the seismic procedure is first developed and then through an example the whole method (dam construction, reservoir filling plus seismic loading) of analysis is assessed.     

Finite element based coupled mode initial post-buckling analysis of a composite cylindrical shell

This paper presents a finite element formulation of Koiter's initial post-buckling theory using a multi-mode approach. Initial post-buckling theory provides direct information about the imperfection sensitivity of a structure under compressive loading, and is also the basis of a nonlinear reduced order model. The objective of the present work is to illustrate the capability of the implementation for buckling analysis of shell structures including modal interaction. A coupled mode initial post-buckling analysis for a composite cylindrical shell under axial compression, including the effect of a nonlinear pre-buckling state, has been carried out using a small number of representative modes. For small imperfection amplitudes the limit-point buckling loads obtained with the reduced order model compare reasonably well with full model nonlinear analysis, illustrating that a fast prediction of the coupled mode response of imperfect shells is possible using the approach proposed.     

考虑结构面震动劣化的岩质边坡动力稳定分析

 通过试验获取结构面震动劣化效应的数学表达式,并将之运用于岩质边坡的动力稳定性分析中。采用3DEC作为计算引擎,在每一动力计算时步内根据动力响应值实时刷新结构面的强度参数,同时由网格净节点力的矢量计算获取该时刻作用于边坡岩体上的地震惯性力。根据极限平衡理论计算该瞬时岩质边坡的稳定性系数,通过动态计算获取整个地震历时过程的稳定性系数时程曲线,以最小平均安全系数作为最终动力稳定性评价指标,从而提出一种考虑结构面震动劣化的岩质边坡动力稳定性计算方法。将该方法运用于汶川地震区岩质边坡实例研究中,稳定性分析结果与实际地质调查情况相符,验证该方法的可行性和工程实用性。     

短程线型单层球面网壳结构在地震作用下的动力稳定性

基于全过程非线性动力反应时程分析方法,对短程线型单层球面网壳结构在地震作用下的动力稳定性进行了系统研究,考虑了不同参数对其动力稳定性影响,其中包括:水平地震作用、竖向地震作用和三向地震作用的影响,材料非线性、矢跨比、初始几何缺陷、杆件截面、支座条件、结构阻尼和不同地震波等的影响,得出了一些有意义的结论,可为网壳工程设计提供参考。     

张弦桁架的动力稳定性与振动控制研究

分析了张弦桁架在水平周期激励下的动力失稳特性,为控制张弦桁架的动力反应,研究了粘弹性阻尼器在该类结构中的应用。提出了粘弹性阻尼器参数的设计方法,给出了张弦桁架施加粘弹性阻尼器的设计曲线。编制了张弦桁架结构的非线性动力时程分析软件,可以计算预应力钢结构施加粘弹性阻尼器后的各种动力反应,提供了一种张弦桁架结构振动控制分析工具和设计方法。     

On nonlinear thermal buckling analysis of cylindrical shells

In this article, the nonlinear buckling behavior of imperfect cylinders made of isotropic, composite and functionally graded materials is studied. A continuum-based semi-analytical finite element formulation is introduced to study the nonlinear behavior of cylinders under thermal loads. A method is proposed to implement the initial geometric imperfection of the cylinder by transformation of structure due to deformation gradients. The influences of geometrical parameters, different materials and imperfection factors are investigated on pre- and post-buckling paths. A comparison is made between the classical von Kármán-based and continuum-based approaches to ensure the validation of the results and to study the applicability of the von-Kármán approximation.     

单层网壳结构动力稳定性分析方法

本文系统分析了单层网壳结构动力稳定性的研究方法。论证了对于在复杂荷载作用下非线性、多自由度复杂结构的动力稳定性问题,基于严格数学定义的Lyapunov运动稳定性理论目前尚不能提供有效的判别准则。通过理论分析和计算指出“刚度矩阵的正定与负定”不足以判定结构是否动力失稳。提出了动力响应全过程曲线的概念,并以此曲线为基础结合结构的时程响应曲线来判定网壳结构的动力稳定性。通过对不同类型荷载、不同计算条件下的网壳结构的弹性和弹塑性动力稳定性的分析,验证了本文所提判别方法的合理性。     

强震区高混凝土面板堆石坝地震残余变形与动力稳定分析

采用三维非线性动力有限元分析方法,针对西部强震区的积石峡水电站工程的高混凝土面板堆石坝,在地震反应分析基础上,应用所建立的分析方法,重点研究了该坝的地震残余变形、坝体单元抗震安全性、面板及坝坡的抗震稳定性,得出了大坝地震残余变形和动力稳定的有关规律和结论,可供工程建设参考。     

钢管结构K型相贯节点的静动态极限承载力

平面K型节点是钢管结构节点主要形式之一。对平面K型圆钢管搭接节点在静力荷载和冲击荷载作用下的弹塑性响应和极限承载力进行了非线性有限元分析。首次得到相贯节点的动力极限承载力,发现节点的动力极限承载力一般小于静力极限承载力。K型圆钢管搭接节点在静、动荷载作用下弹塑性力学特性有较大的区别,节点动力破坏主要发生在节点相贯处,规范计算公式给出的节点静力极限承载力是偏于保守的,所得计算结果和结论对实际工程有一定的应用价值。     

Nonlinear free vibration of skew nanoplates with surface and small scale effects

The nonlinear free flexural vibration of skew nanoplates is studied by considering the influences of free surface energy and size effect (small scale) simultaneously. The formulations are derived based on classical plate theory (CPT) in conjunction with nonlocal and surface elasticity theories using Hamilton's principle. Green's strain tensor together with von Kármán assumptions is employed to model the geometrical nonlinearity. The free surfaces are modeled as two-dimensional membranes adhering to the underlying bulk material without slipping. The solution algorithm is based on the transformation of the governing differential equation from the physical domain to a rectangular computational one, and discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. The effect of small scale parameter and surface effect together with the geometrical parameters and boundary conditions on the nonlinear frequency parameters of the skew nanoplates are studied.