Triangular higher-order element for better prediction of stress resultants and stresses in plated and shell structures

Although they furnish accurate displacements, conventional displacement-based lower order finite elements fail to predict accurate stress resultants and stresses in certain classes of plate and shell problems that involve free edges, steep stress gradients and singularities. In order to tackle such problems, a triangular higher-order shell element based on the nodal basis approach has been developed. The nodes of the element are located at optimal points and its more superior shape functions derived from orthogonal Proriol polynomials. To illustrate the improved performance of the higher-order element as compared to commonly used lower order shell elements in predicting the variations of stress resultants and stresses, three example problems involving a simply supported skew plate, a corner supported square plate, and a clamped cylindrical shell are solved. The stress resultants and the stresses furnished by the higher-order element for the problems considered are found to be accurate with the satisfaction of the natural boundary conditions and devoid of any oscillations. When compared to lower order elements, the higher-order element requires a simple mesh design and lesser degrees of freedom resulting in a considerable reduction in the computational effort, especially for large scale nonlinear analysis.     

Vibration Finite Element Analysis of Bimodular Laminates Using a Higher-Order Plate Theory

Abstract: In this work, a simple C° isoparametric higher-order plate element is developed to study the free vibration analysis of bimodulus laminated plates. The eqriations of motion for the higher-order plate theory are also derived variationally. The warping of cross section and transverse shear deformation are both considered. The natural frequencies and neutral surface locations are determined for benchmark problems. Compared with available analytical solutions, fast convergence and excellent agreement are observed for the present finite element formulation.     

基于PZT-SLDV测试系统的纤维复合板损伤识别研究

为对纤维复合板损伤识别进行研究,采用PZT-SLDV模态测试系统,以存在凹痕损伤四边固定约束的纤维复合板为例,对纤维复合板的损伤检测进行试验和数值模拟研究。通过表面黏贴压电陶瓷(PZT)片对纤维复合板进行激励,再利用SLDV测得其各阶位移模态,并应用中央差分法计算曲率模态进行纤维复合板的损伤识别;最后,利用ABAQUS有限元分析软件,建立含损伤的四边固定约束纤维复合板有限元模型,并对建立的有限元模型进行模态分析。研究结果表明：采用PZT-SLDV测试系统可以有效识别纤维复合板的凹痕损伤;对于频率越高的模态,采用曲率模态的方法识别损伤效果越明显;试验与数值模拟在四边固定约束边界各阶振型的吻合度较高,验证有限元计算模型的正确性。     

A methodological approach for finite element modeling of pretensioned concrete members at the release of pretensioning

This paper presents a methodological approach for finite element simulation of pretensioned concrete members. The three-dimensional analysis presented in this paper involves a rectangular [150 mm (6 in.) tall × 150 mm (6 in.) wide × 2440 mm (96 in.) long] concrete member hosting one 15-mm (0.6 in.) diameter 7-wire low-relaxation Grade 1860 MPa (270 ksi) prestressing strand. The finite element models are divided into two general classifications: (i) concentrically pretensioned, and (ii) eccentrically pretensioned. The finite element models are analyzed based on elastoplastic material behaviors as well as mesh sensitivity. Two approaches are examined for finite element modeling of the pretensioned concrete specimens: (i) the extrusion technique utilizing friction-based contact simulations, and (ii) the embedment technique simulating equivalent responses while being a computationally less expensive solution. A comparative analysis is presented to measure the validity as well as accuracy of the findings by the finite element techniques against the commonly used closed-form solutions based on elastic beam theory. The validity of the finite element approach is further verified by comparative analysis of the analytical data against the experimental findings. The paper concludes that the embedment technique provides an accurate and numerically efficient alternative in comparison with the extrusion method for the simulation of the pretensioned concrete members. While the extrusion technique provides more detailed information corresponding to the regions located immediately around the prestressing strands, including the interface overstresses and bond slippage, the embedment technique appears to have the ability to simulate the overall response of the concrete members with comparable accuracy.     

A GRAPH-THEORETIC MODEL FOR FINITE ELEMENTS WITH SIDE VARIABLES

Most finite elements have variables associated with corner nodes. However, families of equilibrium and hybrid elements exist that have connections on sides, or interfaces, and retain the corner nodes only to describe the geometry. The aim of this paper is to combine concepts from finite elements and graph-theory so that models composed of such elements can be rigorously derived. Two tree graphs are introduced to each element to represent two distinct types of generalized through (forces and moments) and across (translations and rotations) variables. These variables are termed basic and higher-order and are associated with element properties in the form of mukiterminal representations. The terminal equations couple the variables from the two graphs, and are based on weak integral forms, although discrete versions based on graph-theoretic models are also possible. The variables satisfy vertex and circuit laws for each system graph as built up from connected elements, along with driver edges that represent specified loads and displacements. Graph-theory issues are invoked to obtain independent equations for stiffness and flexibility methods of analysis.     

Long-term deflection of cracked composite beams with nonlinear partial shear interaction — A study using neural networks

A new study of the short- and long-term deflections of simply-supported composite beams using finite element analysis and artificial neural networks (ANNs) is presented. In this study, two ANN models are developed and trained using the results of a finite element model developed by the authors in a companion paper. The finite element model accounted for the nonlinear load–slip relationship of shear connectors as well as the creep, shrinkage, and cracking of concrete slabs. The effects of creep and shrinkage of the concrete slab are considered only for non-cracked concrete. A large database representing a wide range of different design parameters was constructed for the purpose of training and verifying the two ANN models. It was found that the two ANN models were capable of predicting deflections of composite beams not used as part of the training process. The ANN models were then used to evaluate the effects of non-geometric design variables on the short- and long-term deflections of simply-supported composite beams. Finally, the short- and long-term deflections computed based on the approaches given in the AISC specification and Eurocode 4 were assessed using the results of the finite element model. It was found that the AISC approach underestimates short-term deflections and overestimate long-term deflections when compared with the results of the finite element method.     

Variable complexity design of composite fuselage frames by response surface techniques

Curved frame structures are often used as part of the internal skeletal structure in aircraft. Laminated composite materials offer potential weight savings for such structures, but composite frames have different and more complex failure mechanisms than metallic frames. In particular, failure mechanisms involving interlaminar stresses are important in composite structures. Interlaminar stresses can be directly computed from three-dimensional finite element models, but the computational expense of these models is prohibitive. In this work, two- and three-dimensional (2D and 3D) finite element models are combined to reduce the computational expense associated with designing composite frames. A response surface design approach is used to approximate the failure response of curved composite C-section frames subjected to an axial tensile loading using a minimum number of finite element analyses. Results are presented for two examples with two and five design variables, respectively.     

Dynamic instability behavior of laminated hypar and conoid shells using a higher-order shear deformation theory

In the present investigation, dynamic instability behavior is studied for the two laminated composite shells having twist radius of curvature, viz., hypar (hyperbolic paraboloid bounded by straight lines, HYP) and conoid (CON). A higher-order shear deformation theory is employed in the C⁰ finite element formulation. Higher-order terms in the Taylor’s series expansion are used to represent the higher-order transverse cross sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effect of transverse shear. The boundaries of dynamic instability regions are obtained using Bolotin’s approach. The structural system is considered to be undamped. The correctness of the formulation is established by comparing the authors’ results of problems with those available in the published literature. The effects of different parameters are studied on the dynamic instability regions of laminated HYP and CON shells.     

Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.     

T形矩管节点不同强化方式的力学性能研究

研究了矩管钢管桁架T形强化节点的基本受力特征和性能差异,借助大型通用有限元程序ADINA,建立了无强化与4种不同的强化方式共5组不同构造参数的T形连接节点数值模型,结合节点实际受力状况分别考虑单向轴力、单轴拉压作用以及拉压轴力与水平干扰力组合作用三种工况,进行了极限承载力和滞回性能的数值分析计算,得出外套管强化节点具有相对较好的综合力学性能,可为类似工程节点强化构造设计以及后续矩管桁架强化节点试验研究提供参考.     

基于曲率模态的钢筋混凝土梁多点损伤位置识别

采用曲率模态对钢筋混凝土梁的多点损伤位置进行了识别研究。首先用有限元程序建立结构模型,并计算出位移模态振型,然后用差分法计算出曲率模态;同时对实际结构进行检测,得到结构的振型并计算出曲率模态。通过有限元模型和实际结构的曲率模态计算得到结构损伤因子,通过分析该损伤因子,可以判断实际结构的损伤位置。数值模拟算例分析表明,曲率模态对结构的损伤较敏感,用该方法识别结构的多点损伤位置是行之有效的。     

曲线箱梁桥空间预应力效应分析

曲线箱形梁桥是空间复杂受力的结构体系,预应力效应一方面能提高构件的承载能力,另一方面也可能对结构带来一些不利的影响。采用三维实体单元和杆单元相结合的空间组合有限元方法,对一座两跨曲线预应力混凝土箱形连续梁桥进行空间受力分析。针对曲线箱形梁的力学特点,对空间曲线钢束摩阻损失的计算方法进行分析。采用组合有限元法和简化方法分析预应力径向力对箱梁腹板的作用效应,比较两者的计算结果差异。采用两种计算模型,分析了预应力对支座受力的影响,对径向支座间距设置和改善支座受力的方法进行了研究。根据预应力效应的分析结果,得到了一些有益的结论,为进一步完善曲线预应力混凝土箱梁桥的设计提供了依据。     

基于耦合模式下初始后屈曲分析的复合柱形壳的有限元分析

运用多模式预测方法,基于Koiter初始后屈曲理论提出了一个有限元公式。初始后屈曲理论提供了压力作用下结构缺陷敏感性的直接信息,同时也是非线性降阶模型的理论基础。研究的目的在于说明包含了模态作用在内的壳结构的屈曲承载力分析。利用一部分有代表性的模态模型,对包含非线性前屈曲效应的轴压作用的复合柱形壳进行了耦合模式下的初始后屈曲分析。当结构缺陷较小时,从降阶模型中得到的极限屈曲荷载与从全模型非线性分析中得到的结果具有良好的一致性,这说明可以运用本文提议的方法对带有缺陷的壳结构的耦合模态响应进行快速的预测。     

Two-dimensional computational framework of meso-scale rigid and line interface elements for masonry structures

In this paper, rigid elements along with nonlinear line interface elements are utilized to model masonry structures. The modeling approach focuses on two dimensions (2D) whereby the in-plane behavior of components is represented by rigid elements and nonlinear line interfaces instead of modeling by a traditional finite element method. In this approach, the component will be allowed to crack in predefined paths which have more likelihood for propagation. The paper discusses the model derivation and implementation. Moreover, the mesh sensitivity of this method is assessed by using different mesh sizes, and it is shown that the model captures response obtained by the experimental tests. The traditional finite element method is indeed capable of predicting the behavior of large scale masonry component, but the computational time is very high. In this study it has been shown that using rigid elements along with nonlinear line interfaces leads to a reduced number of degrees-of-freedom, which consequently reduces the computational time. The material model is implemented in a user-defined subroutine that is compiled with DIANA. The algorithms and material models are validated with well-documented experimental studies, and results clearly show the capabilities of the proposed procedures.     

Probabilistic capacity model and fragility estimates for composite floor systems subjected to column loss

This paper presents probabilistic capacity models for composite floor systems subjected to column loss. The probabilistic capacity models are formulated by adding explanatory terms to an existing deterministic model. The explanatory terms are selected to correct the bias in deterministic capacity model. After that, virtual experiment data generated from finite element simulations are used to calibrate the model parameters. The finite element models consider the effect of axial loading on steel connection and the slab membrane action. The calibration of model parameters is conducted using the Bayesian inference approach. As an application and validation of the probabilistic capacity models, fragility analyses of typical composite floor systems are carried out. The developed fragility curves are compared with those from finite element analysis cooperated with Monte Carlo simulation. The comparison results show that the proposed capacity models are considered reasonable in predicting the resistance capacity of the composite floor and seek a compromise between model accuracy and computational efficiency. The proposed capacity models can be used to carry out a rapid fragility analysis against progressive collapse.     

Parametric stress distribution and displacement functions for tall buildings under lateral loads

In this study, effects of applying higher order axial displacement distribution to solve a continuum model for static analysis of the combined system of framed tube, shear core and outrigger–belt truss system in high‐rise buildings are investigated. Framed tube system is modeled using an orthotropic box beam analogy approach and the interaction between shear core and outrigger–belt truss system on framed tube is modeled with rotating spring placed at outrigger–belt truss location. The axial displacement distributions in web and flange panels along structure's height are proposed to be fifth‐order and fourth‐order polynomials, respectively. Analytic analyses are carried out on the basis of the principle of minimum potential energy. A detailed work is carried out through two numerical examples and the accuracy of proposed approximation functions is compared with previous work and finite element analysis. Results demonstrate that the proposed parametric stress distribution and displacement functions are more accurate than previously proposed functions in comparison with the finite element solution. Copyright © 2012 John Wiley & Sons, Ltd.     

Reliability assessment of cable-stayed bridges based on structural health monitoring techniques

This paper presents the reliability analysis approach of long-span cable-stayed bridges based on structural health monitoring (SHM) technology. First, the framework of structural reliability analysis is recognised based on SHM. The modelling approach of vehicle loads and environmental actions and the extreme value of responses based on SHM are proposed, and then models of vehicle and environmental actions and the extreme value of inner force are statistically obtained using the monitored data of a cable-stayed bridge. For the components without FBG strain sensors, the effects and models (extreme values) of dead load, unit temperature load, and wind load of the bridge can be calculated by the updated finite element model and monitored load models. The bearing capacity of a deteriorated structure can be obtained by the updated finite element model or durability analysis. The reliability index of the bridge's critical components (stiffening girder in this study) can be estimated by using a reliability analysis method, e.g. first order reliability method (FORM) based on the models of extreme value of response and ultimate capacity of the structure. Finally, the proposed approach is validated by a practical long-span cable-stayed bridge with the SHM system. In the example, reliability indices of the bridge's stiffening girder at the stage after repair and replacement after 18 years of operation, and the damaged stage are evaluated.     

Advanced model for predicting the fire response of concrete filled tubular columns

In this work, a nonlinear finite element three-dimensional model is presented and validated in order to study the behaviour of axially loaded concrete filled tubular (CFT) columns with circular cross-section exposed to fire. A realistic sequentially coupled nonlinear thermal-stress analysis is conducted for a series of columns available in the literature. The model is validated by comparing the simulation results with the real fire resistance tests. By means of this model, and extensive sensitivity analysis is performed over a wide range of aspects concerning the finite element modelling of the problem under study, including new key factors not studied previously. Based on this sensitivity analysis several modelling recommendations are given in this paper, which will be useful for future research work. The validated numerical model is furthermore employed to study and discuss the Eurocode 4 Part 1–2 simple calculation model, which is deeply analysed in this paper.     

深部软岩工程大变形力学分析设计系统

采用飞箭软件公司的有限元程序自动生成系统作为软件开发平台，进行“深部软岩工程大变形力学分析设计系统”的合作开发工作。该软件系统具有如下特色：（1）以和分解有限变形力学分析模型为主体，包括极分解力学分析模型供用户进行对比分析；（2）强调非线性大变形力学设计特色：力学对策设计、过程设计和参数设计；（3）包括多种岩土材料本构模型和工程材料单元，可以进行边坡工程、地基工程、地下洞室工程等大变形力学分析；（4）具有我国自主知识产权。目前该软件的弹性、弹塑性大变形二维计算程序和界面已经开发完成。通过对典型算例的弹性数值分析，验证大变形程序的正确性。该软件系统的问世，可为深部软岩巷道等岩体大变形力学问题提供具有分析和设计功能的数值分析软件系统。     

浅析水工混凝土温控防裂措施

给出了有限元分析方法中的混凝土裂缝模型及其应力应变关系，以较好地模拟水工混凝土的开裂作用，从而有利于利用有限元法进行仿真分析，然后结合实际工程阐述了水工混凝土温度控制与防裂的技术措施，供相关人员参考。