Time-dependent creep and shrinkage analysis of composite beams curved in-plan

This paper develops a numerical formulation for the time-dependent creep and shrinkage analysis of steel–concrete composite beams that are curved in-plan under conditions of service load. The creep behaviour of the concrete is considered by using the viscoelastic Wiechert model, in which the aging effect of the concrete is taken into account. The curved composite beam model that is developed also accounts for the partial shear interaction at the deck-girder interface in the tangential (or longitudinal) direction, as well as in the radial (or horizontal) direction, due to the flexibility of the shear connectors. Models based on the developed formulation are validated by comparisons with sophisticated and computationally intensive ABAQUS shell element models, and with available results reported in the literature. The effects of initial curvature and partial interaction on the time-dependent behaviour of curved composite beams are also illustrated in the examples.     

Constitutive modeling of concrete in finite element analysis

Approaches generally used in defining constitutive relations for concrete are reviewed. A computer program developed for the three-dimensional finite element analysis of complex reinforced, prestressed, and refractory concrete systems is described. The constitutive models based on isotropic elastic, orthotropic elastic, and plasticity formulations, which are implemented in that program, are discussed in detail. The program incorporates nonlinear material properties, cracking in concrete, shear transfer in cracked reinforced concrete sections, and time dependent effects such as creep, shrinkage, and transient temperature distributions. A wide range of structural problems are analyzed to demonstrate the applicability of the computer program. Comparisons between predictions with different constitutive models, and between predictions and test results are made.     

A curvilinear triangular finite element for plate bending by a hybrid method of assumed displacements supplemented with assumed stresses

A curvilinear triangular finite element is described for plate bending problems. The geometry is in quadratic parametric representation. The method employs assumed displacements supplemented with assumed stresses and is embedded in Kirchhoff theory.The curvilinear finite element is designed to pass exactly the patch test for constant curvature changes when the flexural rigidity is constant. Rigid body movements are always exactly recovered. Numerical evidence is provided on patch tests for linearly varying curvature changes     

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.     

Creep simulation of asymmetric effects at large strains by stress mode decomposition

The paper presents a framework for creep modelling at large strains of materials exhibiting different behaviours in different loading scenarios, such as tension, compression and shear, respectively. To this end a flow rule is postulated within a thermodynamic consistent framework in a mixed variant formulation and decomposed into a sum of weighted stress mode related quantities. The different stress modes are chosen such that they are accessible to individual examination in the laboratory, where tension, compression and shear are typical examples. The characterisation of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the Lode angle, such that stress mode dependent scalar weighting functions can be constructed. Furthermore the numerical implementation into a finite element program of the constitutive equations is briefly described. In three finite element examples the proposed model is applied to investigate the asymmetric relaxation behaviour of a square plate with circular hole and also the evolution of creep damage in a short cantilever with hole and a gasturbine blade.     

Cosserat Rods with Projective Dynamics

We present a novel method to simulate Cosserat rods with Projective Dynamics (PD). The proposed method is both numerically robust and accurate with respect to the underlying physics, making it suitable for a variety of applications in computer graphics and related disciplines. Cosserat theory assigns an orientation frame to each point and is thus able to realistically simulate stretching and shearing effects, in addition to bending and twisting. Within the PD framework, it is possible to obtain accurate simulations given the implicit integration over time and its decoupling of the local‐global solve. In the proposed method, we start from the continuous formulation of the Cosserat theory and derive the constraints for the PD solver. We extend the standard definition of PD and add body orientations as system variables. Thus, we include the preservation of angular momentum, so that twisting and bending can be accurately simulated. Our formulation allows the simulation of different bending behaviors with respect to a user‐defined Young's modulus, the radius of the rod's cross‐section, and material density. We show how different material specifications in our simulations converge within a few iterations to a reference solution, generated with a high‐precision finite element method. Furthermore, we demonstrate mesh independence of our formulation: Refining the simulation mesh still results in the same characteristic motion, which is in contrast to previous position based methods.     

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.     

A refined model of longitudinally reinforced metal composite wall-beams under steady creep conditions

This paper provides equations describing, to a different degree of accuracy, the bending behavior of longitudinally reinforced metal-composite beams-walls, working under conditions of the steady creep of materials of all phases of composition. From these equations, as partial cases, the correlations of the Bernoulli theory and two versions of the Timoshenko theory are obtained. For statistically definable beams, a simplified version of the specified theory has been developed. Based on the cases of the study of the flexural deformation of hinge-based beam-walls, it is demonstrated that there are such metal compositions, which when used, means that neither classical theory, nor either of the two variants of Timoshenko’s theory can guarantee reliable results regarding amenability even within a 20% level of accuracy, thought of as accessible in the study of the mechanical behavior of structures under the conditions of a steady creep. However, to make reliable calculations, the use of specified theories is needed, allowing for the calculation of the edge effects arising in phase materials in the neighborhood of supporting cross sections.     

Finite element simulation of thermal cracking in massive hardening concrete elements using degree of hydration based material laws

In massive hardening concrete elements, early age thermal cracking due to the heat of hydration might occur. At Ghent University, a simulation procedure is developed, based on the degree of hydration as a fundamental parameter. This parameter is related with the microstructural development during cement hydration. Accurate finite element simulations are obtained for the problem of early age thermal cracking, applying a staggered analysis. The time dependent material behaviour is implemented by means of a Kelvin chain. The cracking behaviour is implemented using a smeared cracking approach with non-linear softening behaviour. The results of the model are verified experimentally.     

Variation of stress resultants in concrete structures due to time-dependent creep and shrinkage strains of concrete

A general procedure for calculating the variation with time of the internal stress resultants and hence the stresses, in concrete structures is discussed. In particular, a study is made of the changes in the stress resultants due to time-dependent creep and shrinkage strains of concrete.A general procedure of calculating the variation in the stress resultants due to differential creep strains in concrete structures has been proposed by the author[1]. A similar procedure is followed in this paper to study these variations when creep and shrinkage strains take place simultaneously.The method leads to a system of n-linear differential equations of the form: X = AXt + B the solution of which is performed by a computer using Runge-Kutta numerical procedures.A reinforced concrete portal frame exhibiting creep and shrinkage strains is solved by the proposed method and the results are given in tabular and graphical form.     

A critical comparison of several numerical methods for computing effective properties of highly heterogeneous materials

Modelling transport and long-term creep in concrete materials is a difficult problem when the complexity of the microstructure is taken into account, because it is hard to predict instantaneous elastic responses. In this work, several numerical methods are compared to assess their properties and suitability to model concrete-like microstructures with large phase properties contrast. The methods are classical finite elements, a novel extended finite element method (μ-xfem), an unconstrained heuristic meshing technique (amie), and a locally homogenising preprocessor in combination with various solvers (benhur). The benchmark itself consists of a number of simple and complex microstructures, which are tested with a range of phase contrasts designed to cover the needs of creep and transport modelling in concrete. The calculations are performed assuming linear elasticity and thermal conduction. The methods are compared in term of precision, ease of implementation and appropriateness to the problem type. We find that xfem is the most suitable when the mesh if coarse, and methods based on Cartesian grids are best when a very fine mesh can be used. Finite element methods are good compromises with high flexibility.     

破片侵彻飞机机翼壁板的应急修理有限元分析

针对飞机机翼壁板遭受导弹破片侵彻后的应急修理问题,以某飞机机翼受损壁板为例,采用全机有限元模型对其铆接修理进行强度计算．计算模型中补片的单元类型采用壳单元,铆钉用梁单元．结果表明,在铆钉钉距、排距和边距一定的情况下,铆钉排数与修理后的承载能力有对应关系．该对应关系为战场上合理制定应急修理方案提供理论参考．     

Bridging art and engineering using Escher-based virtual elements

The geometric shape of an element plays a key role in computational methods. Triangular and quadrilateral shaped elements are utilized by standard finite element methods. The pioneering work of Wachspress laid the foundation for polygonal interpolants which introduced polygonal elements. Tessellations may be considered as the next stage of element shape evolution. In this work, we investigate the topology optimization of tessellations as a means to coalesce art and engineering. We mainly focus on M.C. Escher’s tessellations using recognizable figures. To solve the state equation, we utilize a Mimetic Finite Difference inspired approach, known as the Virtual Element Method. In this approach, the stiffness matrix is constructed in such a way that the displacement patch test is passed exactly in order to ensure optimum numerical convergence rates. Prior to exploring the artistic aspects of topology optimization designs, numerical verification studies such as the displacement patch test and shear loaded cantilever beam bending problem are conducted to demonstrate the accuracy of the present approach in two-dimensions.     

A class of C finite elements for the static and dynamic analysis of laminated plates

A general higher-order deformation theory is developed to analyse the behaviour of an arbitrary laminated fibre-reinforced composite plate. Three-dimensional effects such as the warping of sections and the presence of interlaminar stress field components are taken into account assuming a power series expansion of displacements along the thickness. A class of C⁰ finite element models based on this theory is then developed for mono- and bi-dimensional elements. Applications of the models to bending and vibration of laminated plates are then discussed. The present solutions are compared with those obtained using the three-dimensional elasticity theory, classical laminate theory and other higher-order theories.     

A Damage mechanics constitutive theory for the inelastic behaviour of concrete

A rate-independent constitutive theory for the behaviour of concrete in the inelastic range is proposed. It is based on damage mechanics concepts previously applied to rock materials by the author. The inelasticity is provided by two basic damage mechanisms, namely, shear damage and hydrostatic tension damage. A scalar damage parameter is used to represent the degradation of the elastic properties. In addition to the damage mechanisms, a plasticity yield surface is included to bound the model in the hydrostatic compression sense. A simple calibration procedure is presented and the model is shown to predict reasonable behaviour for a variety of monotonic and reversed loading paths. The model is readily implemented in finite element codes and a number of representative boundary value problems is solved. Suggestions for future developments conclude the paper.     

Cable stretching force optimization of concrete cable-stayed bridges including construction stages and time-dependent effects

This paper presents an optimization algorithm to compute the prestressing forces on concrete cable-stayed bridges to achieve the desired final geometry. The structural analysis includes the load history and geometry changes due to the construction sequence and the time-dependent effects due to creep, shrinkage and aging of the concrete. An entropy-based approach was used for structural optimization and discrete direct sensitivity analysis was used to evaluate the structural response to changes in the design variables. Numerical examples are presented and the results exhibit the importance of considering both the construction stages and the time-dependent effects for adequately predict the bridge behaviour and compute the cable prestressing forces.     

A layered cylindrical quadrilateral shell element for nonlinear analysis of RC plate structures

This paper proposes a simple and accurate 4-node, 24-DOF layered quadrilateral flat plate/shell element, and an efficient nonlinear finite element analysis procedure, for the geometric and material nonlinear analysis of reinforced concrete cylindrical shell and slab structures. The model combines a 4-node quadrilateral membrane element with drilling or rotational degrees of freedom, and a refined nonconforming 4-node 12-DOF quadrilateral plate bending element RPQ4, so that displacement compatibility along the interelement boundary is satisfied in an average sense. The element modelling consists of a layered system of fully bonded concrete and equivalent smeared steel reinforcement layers, and coupled membrane and bending effects are included. The modelling accounts for geometric nonlinearity with large displacements (but moderate rotations) as well as short-term material nonlinearity that incorporates tension, cracking and tension stiffening of the concrete, biaxial compression and compression yielding of the concrete and yielding of the steel. An updated Lagrangian approach is employed to solve the nonlinear finite element stiffness equations. Numerical examples of two reinforced concrete slabs and of a shallow reinforced concrete arch are presented to demonstrate the accuracy and scope of the layered element formulation.     

A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators: Bending and free vibrations

This paper addresses the bending and free vibrations of multilayered cylindrical shells with piezoelectric properties using a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elasticity theory. In the present 3D axisymmetric model, the equations of motion are expressed by expanding the displacement field using Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.     

广州新电视塔结构健康监测应变修正计算的研究

大型钢筋混凝土结构做长期的结构健康监测,需要综合考虑混凝土的收缩徐变影响.对应变传感器采集的原始应变数据做适当的修正,可提高监测的准确度.本文以广州新电视塔结构健康监测中应变修正的计算为例,阐述了美国混凝土学会(ACI)推荐的收缩徐变分析理论在结构健康监测中的应用,并结合实验室的试件测试数据,修正徐变和收缩的具体计算公...     

Study of elastic behaviour of plates containing cracks by finite element analysis

This work applies finite element analysis very simply to cracked plates. An infinite plate and a finite plate, both with a central crack, are considered to study their elastic behaviour and some fracture mechanics concepts, such as the geometry factor and the fracture toughness. These magnitudes are calculated by means of finite element methods and the results are in very good agreement with the established theory, which proves that the finite element approach is very appropriate. The fracture toughness fraction is defined and calculated for a finite plate to predict its failure.