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.     

Dynamic response simulation for reinforced concrete slabs

Present investigation comprises development of a new finite element numerical formulation for nonlinear transient dynamic analysis of reinforced concrete slab structures. Depending on many experimental data, new material constitutive relationships for concrete material have been formulated. A regression analysis of available experimental data in the SPSS-statistical program has been employed for formulating the proposed material finite element models, and the appropriateness of the models are confirmed through the histograms and measured indices of determination. Concrete slab structures were analyzed using eight-node serendipity degenerated plate elements. The constitutive models of the nonlinear materials are introduced to take into account the nonlinear stress–strain relationships of concrete. For studying the stress profile of the concrete slab through its thickness, a layered approach is adopted. Elastic perfectly plastic and strain hardening plasticity approaches have been employed to model the compressive behavior of concrete. Assumptions for strain rate effect were included in dynamic analysis by supposing the dynamic yield function as a function of the strain rate, in addition to be the total plastic strain. The yield condition is formulated in terms of the first two stress invariants. Geometrical nonlinearity was considered in analysis as a mathematical model based on the total lagrangian approach taking into account Von Karman assumptions. Implicit Newmark with corrector–predictor algorithm was used for time integration solution of the equation of the motion for slab structures. An incremental and iterative procedure is adopted to trace the entire response of the structure; a displacement convergence criterion is adopted in the present study. A computer program coded in FORTRAN has been developed and used for the dynamic analysis of reinforced concrete slabs. The numerical results show good agreement with other published studies’ results which include deflections.     

Time-dependent modelling of RC structures using the cracked membrane model and solidification theory

A non-linear finite element model is presented for the time-dependent analysis of reinforced concrete structures under service loads. For the analysis of members in plane stress, the model is based on the cracked membrane model using a rotating crack approach combined with solidification theory for modelling creep. The numerical results are compared with a variety of long-term laboratory measurements, including development of deflections and cracking with time in a reinforced concrete beam, time-dependent change in support reactions of a continuous beam subject to support settlement and creep buckling of columns. The numerical results are in good agreement with the test data.     

Nonlinear analysis of reinforced concrete cylindrical shells

In this paper, analysis of reinforced concrete cylindrical shells is performed using a strain-based finite element. The shell element employed is bidimensional, cylindrical circular and has four-nodes and five nodal degrees of freedom. The nonlinearities due to concrete cracking and yielding of the steel are taken into account. The constitutive models for the materials employ the smeared cracking concept and a finite element layered approach. Concrete is modeled by a strain-induced orthotropic-elastic model under plane state of stress. A bilinear steel model is used and the stress/reversal with Baushinger effect is included. Examples show the good accuracy provided by this analysis.     

Finite element stress analysis of a reinforced high-strength concrete column in severe fires

The objective of this study is to quantify the development of thermal stress states that account for the occurrence of moisture-induced explosive spalling of reinforced high-strength concrete structures under rapid heating conditions. Obtained from finite difference models of simulating coupled heat and mass transport phenomena in heated reinforced concrete elements, transient temperature profiles are used as prescribed boundary conditions for subsequent finite element thermo-elastic stress analysis. A computational methodology using the theory of mixtures (volume averaging) is presented to compute thermally induced effective stresses that are potentially associated with thermal spalling of high-strength concrete.     

Analysis of cyclic loading of plane RC structures

A numerical procedure for cyclic loading response of planar reinforced concrete structures is presented. A nonlinear orthotropic stress strain law for biaxially loaded plain concrete is developed and compared with experimental results for monotonic biaxial loading and uniaxial cyclic loading. The stress-strain law recognizes strength and ductility changes due to biaxial stress, and strength and stiffness degradation with cycles of loading. The stress strain law is incorporated into a finite element computer program which utilizes isoparametric quadrilaterals with extra non-conforming deformation modes. Numerical and experimental results are presented for a monotonically loaded shear wall-frame system and a cyclically loaded shear wall.     

Numerical modeling of masonry-infilled RC frames subjected to seismic loads

The behavior of masonry-infilled reinforced concrete frames under cyclic lateral loading is complicated because a number of different failure mechanisms can be induced by the frame-infill interaction, including brittle shear failures of the concrete columns and damage of the infill walls. In this study, nonlinear finite element models have been used to simulate the behavior of these structures. Diffused cracking and crushing in concrete and masonry are described by a smeared-crack continuum model, while dominant cracks as well as masonry mortar joints are modeled with a cohesive crack interface model. The interface model adopts an elasto-plastic formulation to describe the mixed-mode fracture of concrete and masonry. The model accounts for cyclic crack opening and closing, reversible shear dilatation, and joint compaction due to damage. The constitutive models have been validated with experimental data and successfully applied to the dynamic analysis of a three-story, two-bay, masonry-infilled, non-ductile, reinforced concrete frame tested on a shake table. The results have demonstrated the capabilities of the finite element method in capturing the nonlinear cyclic load–displacement response and failure mechanisms of the structure, and indicated the important contribution of infill walls to the seismic resistance of a non-ductile reinforced concrete frame.     

Probabilistic analysis of reinforced concrete columns

The subject of this work is the probabilistic finite element analysis of reinforced concrete columns. Concrete properties are represented as homogeneous Gaussian random fields. The yield stress and position of steel reinforcement, dimensions of the column cross-section and axial load are considered as random variables. The Monte Carlo method is employed to obtain expected values and standard deviations of the rupture load. The partial safety factors method is used for columns design and structural safety is evaluated by means of the reliability index, which is obtained through simulations. The effects of main parameters on the reliability index are investigated. It is shown that the correlation length of random fields for concrete properties may have a significant effect on reliability. Therefore, simplified procedures, which do not consider spatial variations of concrete properties are inappropriate for safety analysis.     

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.     

Nonlinear Formulations of a Four-Node Quasi-Conforming Shell Element

The quasi-conforming technique was introduced in the 1980’s to meet the challenge of inter-elements conforming problems and give a unified treatment of both conforming and nonconforming elements. While the linear formulation is well established, the nonlinear formulation based on the quasi-conforming technique that includes geometric and material nonlinearity is presented in this paper. The formulation is derived in the framework of an updated Lagrangian stress resultant, co-rotational approach. The geometric nonlinear formulation provides solutions to buckling and postbuckling behaviour while the material nonlinear formulation considers the spread of plasticity within the element while maintaining an explicit construction of element matrices. Aside from the elasto-plastic constitutive relation, formulations on laminate composites and reinforced concrete are also presented. The formulations of laminate composite and reinforced concrete material are present based on the layer concept, the material properties can vary throughout the thickness and across the surface of a shell element. The various failure criteria for laminate composite are included in the formulation which makes it possible to analyses the progressive failure of fibre and matrix. For the reinforced concrete material, the nonlinearities as a result of tensile cracking, tension stiffening between cracks, the nonlinear response of concrete in compression, and the yielding of the reinforcement are considered. The steel reinforcement is modeled as a bilinear material with strain hardening.     

火灾后预应力双T板的加固设计

针对遭遇火灾损伤的预应力双T板,运用有限元软件Abaqus进行顺序热-力耦合分析,得到预应力双T板的温度场云图、载荷-位移曲线,以及构件破坏时钢绞线和混凝土的应力云图.对混凝土双T板构件受损程度进行判定,确认其具有加固价值.基于该双T板的受弯承载力、挠度和破坏性质分析,提出体外预应力钢绞线结合增大受压区截面的加固方案,...     

Pre- and post-degradation analysis of composite materials with different moduli in tension and compression

An isoparametric finite element tor the analysis of multi-layer composite materials is presented. Several linear and nonlinear stress-strain relations are discussed. Special attention is given to the composite materials with different moduli in tension and compression, for which a new mathematical model is presented and tested.Different failure criteria for the matrix degradation are incorporated in the element and several post-degradation behaviors are also considered.Finally we discuss the role of the Newton-Raphson method in composite materials, especially in the presence of geometrical nonlinearities.     

高混凝土重力坝孔口应力非线性数值模拟

为准确描述重力坝孔口应力分布,提出高混凝土重力坝孔口应力的非线性数值计算分析整体方案．首先对坝体进行线性计算获得孔口应力分布规律及峰值以便于配筋,然后基于损伤塑性模型对孔口剖面作非线性应力应变分析,考察钢筋应力及其止裂效果．以某钢筋混凝土重力坝工程为背景,依据规范简化混凝土单轴应力一应变曲线,在Abaqus平台上对中孔的3个剖面进行非线性有限元分析,考察中孔在坝体自重和内水压力作用下的结构特性和损伤分布规律等,并重点探讨损伤区域的演化及钢筋应力等问题．结果表明数值模拟结果与模型试验有较好的一致性,可为同类型工程的数值计算和设计提供一定借鉴．     

Weight optimization for flexural reinforced concrete beams with static nonlinear response

The weight optimization of reinforced concrete (RC) beams with material nonlinear response is formulated as a general nonlinear optimization problem. Incremental finite element procedures are used to integrate the structural response analysis and design sensitivity analysis in a consistent manner. In the finite element discretization, the concrete is modelled by plane stress elements and steel reinforcement is modelled by discrete truss elements. The cross-sectional areas of the steel and the thickness of the concrete are chosen as design variables, and design constraints can include the displacement, stress and sizing constraints. The objective function is the weight of the RC beams. The optimal design is performed by using the sequential linear programming algorithm for the changing process of design variables, and the gradient projection method for the calculations of the search direction. Three example problems are considered. The first two are demonstrated to show the stability and accuracy of the approaches by comparing previous results for truss and plane stress elements, separately. The last one is an example of an RC beam. Comparative cost objective functions are presented to prove the validity of the approach.     

A finite element model for the nonlinear analysis of reinforced and prestressed masonry walls

A materially nonlinear layered finite element model is proposed for the analysis of reinforced and/or prestressed masonry wall panels under monotonie loadings in the plane and/or out of the plane, capable of evaluating both the serviceability load and the ultimate load. An orthotropic incrementally linear relationship and equivalent uniaxial concept are used to represent the behaviour of masonry under biaxial stresses while a uniaxial bilinear elasto-plastic model with hardening is employed for rebar and the so-called ‘power-formula’ is adopted to describe the stress-strain relationship of prestressing steel.

After cracking, the smeared coaxial rotating crack model is adopted and tension stiffening, reduction in compressive strength and stiffness after cracking, and strain softening in compression are accounted for. The modified Newton-Raphson iteration method is employed to ensure convergency of non linear solution.

The proposed finite element model has been tested by a comparison with experimental data available in literature, both for reinforced and prestressed wall panels. The analysis of results shows good agreement between the values obtained by the proposed model and those obtained experimentally.     

Elastoplastic analysis of thick perforated plates with application to prestressing anchor heads

The elastoplastic finite element stress analysis of a prestressing anchor head is described. The anchor head constitutes part of an unbonded tendon system for a prestressed concrete nuclear reactor vessel. The anchor head, which is a thick plate with a central region perforated by a large number of holes, is analyzed using an equivalent homogeneous material with numerically determined effective elastic constants and yield stress. Maximum inelastic tensile strains are calculated as a function of anchor head load level, and related to observed failure modes.     

基于APDL的ANSYS嵌入式配筋实现

以ANSYS为平台,应用APDL实现钢筋混凝土有限元模型中钢筋单元嵌入混凝土单元的功能.应用该方法可以在ANSYS中方便地建立复杂的钢筋混凝土分离式模型.利用Newton-Raphson方法求解等参数单元的坐标插值函数中被约束节点在自然坐标系下的坐标值,得到自然坐标系下节点对应形函数值,并将对应的形函数值作为约束方程中混凝土单元节点位移的分项因数,从而实现嵌入节点与被嵌入单元位移协调.计算结果与Marc的算例结果吻合良好,说明该方法合理.