Nonlinear finite element for modeling reinforced concrete columns in three-dimensional dynamic analysis

A new finite element is proposed for slender, flexure-dominated reinforced concrete columns subjected to cyclic biaxial bending with axial load, and its implementation into a program for the nonlinear static or dynamic analysis of structures in three-dimensions, is described. The element belongs to the class of distributed inelasticity discrete models for the nonlinear dynamic response analysis of frame structures to earthquake ground motions. The element tangent flexibility matrix is constructed at each time step by Gauss-Lobatto integration of the section tangent flexibility matrix along the member length. The tangent flexibility matrix of the cross-section relates the increment of the vector of the three normal stress resultants N, M_y, M_z, to the vector increment of the section deformation measures. ε_o, _y, _z, and is constructed on the basis of the bounding surface of the cross-section, which is defined as the locus of points in the space of the normalized N, M_y, M_z, which correspond to ultimate strength. The bounding surface concept enables the model to produce realistic predictions for the nonlinear response of the cross-section to any arbitrary loading path in the space N-M_y-M_z.The bounding surface is introduced and utilized in a very flexible manner, enabling a variety of cross-sectional shapes to be treated in a unified way. As this flexibility is at the expense of computational simplicity and memory size requirements, emphasis is placed on algorithmic techniques to facilitate numerical implementation and to increase computational efficiency.     

Non-linear finite element dynamic analysis of two-dimensional concrete structures

This paper presents a numerical procedure for predicting the non-linear dynamic response of plane and axisymmetric reinforced concrete structures. Isoparametric elements with special embedded axial members are used to discretize concrete and steel in space. A summary of a rate and history dependent constitutive model for progressive failure analysis of concrete is given in which the compression behaviour is modelled as a strain rate sensitive elasto-viscoplastic material and in tension as strain rate dependent linear elastic strain softening material. The different rales governing the pre-failure and post-failure behaviour in compression and tension are developed in which the strain rate dependency is included. Steel is modelled as a strain rate dependent uniaxial elasto-viscoplastic material. Explicit central difference scheme in conjunction with an energy balance check is employed for time integration of equations of motion. A computer program for linear and non-linear dynamic analysis of concrete structures is described. Finally, some numerical applications are presented.     

A finite element approach to global-local modeling in composite laminate analysis

A finite element model is described to study interlaminar stresses within polymer composite laminated materials. This model is based upon a global-local model proposed by Pagano and Soni in 1983. The development of solution procedures includes an out-of-core memory solving technique. The numerical results generated for simple plate problems with and without holes in the center under uniaxial loading are reported. Comments regarding the finite-element mesh-size, numerical stability, problem size and sensitivity of results to substructuring of the laminate into global and local regions have also been discussed.     

Nonlinear finite element analysis of concrete structures using new constitutive models

Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.     

Nonlinear finite element analysis of reinforced concrete stiffened and cellular slabs

A novel approach is presented in this paper for linear and nonlinear finite element analysis of reinforced and prestressed concrete cellular slabs based on a slab-beam model. Mindlin/Timoshenko assumptions are adopted in the slab-beam model which thus allows for transverse shear deformations. Several examples are presented to illustrate the accuracy and limitations of the method.     

不确定性转子系统的随机有限元建模及响应分析

随机特性和随机载荷会引起转子系统动力响应的不确定性,是转子动力学分析中的重要影响因素.本文基于Timosheke梁理论,把转轴的材料和几何随机特性表示为一维随机场函数,推导出随机转轴有限元列式,建立转子系统随机动力学模型,并给出随机载荷作用下随机转子系统动力响应统计量的分析方法.分别对线性和非线性涡轮泵转子系统进行了随机动力响应分析,并同Monte Carlo仿真结果进行对比,结果表明所建立的随机有限元动力学模型和给出的随机响应分析方法是合理可行的,可以有效应用于实际转子系统随机动力学分析和设计中.     

导弹天线罩参数化有限元建模和热可靠性分析

基于Pro/ENGINEER,Patran和MSC Nastran,以坚晶石导弹天线罩为研究对象,结合参数化有限元建模方法,将天线罩结构尺寸、材料性能和热流输入等作为随机因素,使用蒙特卡罗数字模拟法对其进行热可靠性分析,详述参数化建模和可靠性分析的流程,得到天线罩热应力的概率分布、随机因素与热应力的变化关系以及天线罩热可靠度等可靠性分析数据.结果显示,本文的天线罩热可靠度为99.93%.本研究证实对导弹天线罩进行参数化有限元建模和可靠性分析的可行性.     

Flexural analysis of reinforced fibrous concrete members using the finite element method

A numerical procedure based on the finite element method is developed for the geometric and material nonlinear analysis of reinforced concrete members containing steel fibres and subjected to monotonic loads. The proposed procedure is capable of tracing the displacements, strains, stresses, crack propagation, and member end actions of these structures up to their ultimate load ranges. A frame element with a composite layer system is used to model the structure. An iterative scheme based on Newton-Raphson's method is employed for the nonlinear solution algorithm. The constitutive models of the nonlinear material behaviour are presented to take into account the nonlinear stress-strain relationships, cracking, crushing of concrete, debonding and pull-out of the steel fibres, and yielding of the reinforcement. The geometric nonlinearity due to the geometrical change of both the structure and its elements are also represented. The numerical solution of a number of reinforced fibrous concrete members are compared with published experimental test results and showed good agreement.     

Accurate finite element modeling of acoustic waves

In the paper we suggest an accurate finite element approach for the modeling of acoustic waves under a suddenly applied load. We consider the standard linear elements and the linear elements with reduced dispersion for the space discretization as well as the explicit central-difference method for time integration. The analytical study of the numerical dispersion shows that the most accurate results can be obtained with the time increments close to the stability limit. However, even in this case and the use of the linear elements with reduced dispersion, mesh refinement leads to divergent numerical results for acoustic waves under a suddenly applied load. This is explained by large spurious high-frequency oscillations. For the quantification and the suppression of spurious oscillations, we have modified and applied a two-stage time-integration technique that includes the stage of basic computations and the filtering stage. This technique allows accurate convergent results at mesh refinement as well as significantly reduces the numerical anisotropy of solutions. We should mention that the approach suggested is very general and can be equally applied to any loading as well as for any space-discretization technique and any explicit or implicit time-integration method.     

Anisotropic finite element modeling for patient-specific mandible

This paper presents an ad hoc modular software tool to quasi-automatically generate patient-specific three-dimensional (3D) finite element (FE) model of the human mandible. The main task is taking into account the complex geometry of the individual mandible, as well as the inherent highly anisotropic material law. At first, by computed tomography data (CT), the individual geometry of the complete range of mandible was well reproduced, also the separation between cortical and cancellous bone. Then, taking advantage of the inherent shape nature as ‘curve’ long bone, the algorithm employed a pair of B-spline curves running along the entire upper and lower mandible borders as auxiliary baselines, whose directions are also compatible with that of the trajectory of maximum material stiffness throughout the cortical bone of the mandible. And under the guidance of this pair of auxiliary baselines, a sequence of B-spline surfaces were interpolated adaptively as curve cross-sections to cut the original geometry. Following, based on the produced curve contours and the corresponding curve cross-section surfaces, quite well structured FE volume meshes were constructed, as well as the inherent trajectory vector fields of the anisotropic material (orthotropic for cortical bone and transversely isotropic for cancellous bone). Finally, a sensitivity analysis comprising various 3D FE simulations was carried out to reveal the relevance of elastic anisotropy for the load carrying behavior of the mandible.     

Nonlinear finite element analysis of reinforced concrete plates and shells under monotonic loading

Plane stress constitutive models are proposed for the nonlinear finite element analysis of reinforced concrete structures under monotonic loading. An elastic strain hardening plastic stress-strain relationship with a nonassociated flow rule is used to model concrete in the compression dominating region and an elastic brittle fracture behavior is assumed for concrete in the tension dominating area. After cracking takes place, the smeared cracked approach together with the rotating crack concept is employed. The steel is modeled by an idealized bilinear curve identical in tension and compressions. Via a layered approach, these material models are further extended to model the flexural behavior of reinforced concrete plates and shells. These material models have been tested against experimental data and good agreement has been obtained.     

Network-distributed finite element analysis

The widespread availability of local-area networks has made the combined processing power of workstations a viable approach for compute-intensive analyses. In this paper, we describe several distributed algorithms for structural analysis using finite element methods, and we assess their performance on a conventional Ethernet-connected workstation network. Direct, iterative and hybrid equation solvers are evaluated for their performance on plane-elasticity problems, and are contrasted with respect to overall solution time and efficiency in distributing computations over a network. Equations modeling the costs of network communication and structural analysis computations are derived, and are subsequently used to predict the performance of several variations on the implemented algorithms. Our results show that each of the methods performs well on network architectures, and in particular that, while direct methods usually minimize network communication, certain iterative and hybrid methods can often be used to minimize overall solution time.     

埋伏牙正畸半自动逆向建模及有限元分析

为指导埋伏牙治疗的临床正畸操作,进行埋伏牙正畸半自动逆向建模及有限元分析,比较不同牵引方式下埋伏牙的牙周膜应力分布情况．首先基于病例CT扫描数据,利用MIMICS软件荻取粗糙的埋伏牙及颌骨点云数据;然后采用VC＋＋自编程序自动提取精确的模型特征,并导入CATIA中生成埋伏牙、牙周膜及颌骨CAD模型;最后运用ABAQUS对与埋伏牙的牙体长轴成0°,45°及90°等3种方向的正畸牵引方式进行接触分析,得出正畸临床状态下的牙周膜应力大小及分布．结果表明,与牙体长轴成45°方向的牵引方式更适合临床正畸操作;采用逆向工程软件与自编程序相结合的半自动建模方式能提高建模效率和精度．     

Probabilistic fiber element modeling of reinforced concrete structures

A computational model based on a stochastic fiber element model is developed in this study. This model can be utilized for probabilistic evaluation of reinforced concrete (RC) members. The stochastic fiber element model is developed by combining the conventional fiber element formulation and the midpoint method for random field representation, to account for spatial variability of material and geometrical properties within a structural member. Three verification examples show the capability of the developed model in estimating the nonlinear structural behavior including softening. As an application of the developed computational model, a probabilistic strength analysis of a RC column is conducted in terms of the axial load-bending moment interaction. An approach of evaluating RC structural systems using the developed probabilistic computational model is also presented.     

Development of finite element computer code for thermal analysis of roller compacted concrete dams

Thermal analysis of roller compacted concrete (RCC) dams plays an important role in their design and construction. This paper deals with the development of a finite element based computer code for the determination of temperatures within the dam body. The finite element code is then applied to the real full-scale problem to determine the impact of the placement schedule on the thermal response of roller compacted concrete dam. Based on the results obtained, it could be concluded that for a given roller compacted concrete dam, changing the placing schedule can optimize the locations of maximum temperature zones.     

Limit load analysis of thick-walled concrete structures - a finite element approach to fracture

The paper illustrates the interaction of constitutive modelling and finite element solution techniques for limit load prediction of concrete structures.On the constitutive side, an engineering model of concrete fracture is developed in which the Mohr-Coulomb criterion is augmented by tension cut-off to describe incipient failure. Upon intersection with the stress path the failure surface collapses for brittle behaviour according to one of three softening rules — no-tension, no-cohesion, and no-friction. The stress transfer accompanying the energy dissipation during local failure is modeled by several fracture rules which are examined with regard to ultimate load prediction.On the numerical side the effect of finite element idealization is studied first as far as ultimate load convergence is concerned. Subsequently, incremental tangential and initial load techniques are compared together with the effect of step size.Limit load analyses of a thick-walled concrete ring and a lined concrete reactor closure conclude the paper along with engineering examples.     

Solution errors in finite element analysis

The development of the finite element method so far indicates that it is a discretization technique especially suited for positive definite, self-adjoint, elliptic systems, or systems with such components. The application of the method leads to the discretized equations in the form of $\text{u}\text{?}\text{=}\text{f(u)}$, where u lists the response of the discretized system at n preselected points called nodes. Instead of explicit expressions, vector function f and its Jacobian f,_u are available only numerically for a numerically given u. The solution of $\text{u}\text{?}\text{=}\text{f(u)}$ is usually a digital computer. Due to finiteness of the computer wordlength, the numerical solution $\text{u}{}_{\mathrm{c}}$ is in general different from u. Let $\text{u}\text{(}\text{x}\text{, t)}$ denote the actual response of the system in continuum at points corresponding to those of u. In the literature. $\text{u}\text{(}\text{x}\text{, t)-}\text{u}$ is called the discretization errors, $\text{u}\text{-}\text{u}{}_{\mathrm{c}}$ the round-off errors, and the s is. $\text{u}\text{(}\text{x}\text{, t)-}\text{u}{}_{\mathrm{c}}$ is called the solution errors. In this paper, a state-of-the-art survey is given on the identification, growth, relative magnitudes, estimation, and control of the components of the solution errors.     

Geometric uncertainties in finite element analysis

This paper demonstrates the use of automatic differentiation in solving finite element problems with random geometry. In the area of biomechanics, the shape and size of the domain is often known only approximately. Stochastic finite element analysis can be used to compute the variability in the structural response as a result of variability in the shape of the structural domain. Automatic differentiation can be used to compute the shape sensitivites accurately and effortlessly. Unlike randomness in material properties, the response variability can be the same as or greater than the variability in the input. When both the Young's modulus and geometry are random, it is likely that randomness in geometry will dominate randomness in Young's modulus.     

Adaptive p-version based finite element formulations for thermal modeling/analysis of structural configurations

Adaptive p-version based hierarchial finite element formulations in conjunction with a posteriori error estimation concepts are described with emphasis on applicability for thermal modeling/analysis of structural configurations. The basic concepts and formulations of hierarchical p-version finite elements for thermal analysis are first described. A posteriori error estimation features are utilized to steer the process of adaptive refinement. Several configurations comprised of one-dimensional structures are evaluated to validate the applicability of the proposed formulations and to demonstrate the potential of the p-version adaptive formulations for thermal modeling/analysis. The methodology offers potential and promises to be an attractive to conventional finite element thermal modeling/analysis approaches.     

CDM based finite element code for concrete in 3-D

This paper presents a three dimensional finite element code DAMAG3D for nonlinear analysis of concrete type materials modeled as elastic-damage. The CDM model adopted is the one as proposed by SUARIS W, OUYANG C, FERNANDO V. M. Damage model for cyclic loading of concrete. J Engng Mech, American Society of Civil Engineers 1990; 116(5): 1020-35. for monotonic and cyclic loading of concrete structures. Code DAMAG3D is applied to simulate response of concrete under monotonically increasing load paths of uniaxial compression, Brazilian test, strip loading and patch loading, with reasonable correlation established with experimental results and results from other nonlinear constitutive models.