A new algorithm for numerical solution of dynamic elastic-plastic hardening and softening problems

The objective of this paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems, particularly for the implementation of the gradient dependent model used in solving strain softening problems. The new algorithm for the solution of dynamic elastic-plastic problems is derived based on the parametric variational principle. The gradient dependent model is employed in the numerical model to overcome the mesh-sensitivity difficulty in dynamic strain softening or strain localization analysis. The precise integration method, which has been used for the solution of linear problems, is adopted and improved for the solution of dynamic non-linear equations. The new algorithm is proposed by taking the advantages of the parametric quadratic programming method and the precise integration method. Results of numerical examples demonstrate the validity and the advantages of the proposed algorithm.     

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.     

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.     

Some experiences in the use of ADINA in the Swedish Nuclear Industry

This paper presents a number of engineering analysis problems solved from 1990 to 1996 where ADINA was used in the analysis. The problems are in the following areas: natural frequencies, dynamic loading, fatigue, fracture mechanics and natural convection-driven fluid flow. For most of the problems, a comparison between calculations and measurements is also presented. Our experience is that good numerical results can be achieved for static linear problems even when the geometry is complex, but in dynamic analysis it can be difficult to establish models that accurately contain all frequencies, and, of course, in non-linear analysis, the representation of the non-linear material behaviour provides a limit to the modelling accuracy.     

Modelling the dynamical behaviour of a paper web. Part II

In this paper, a finite element procedure is used to study the dynamic behaviour of a paper web in a free span between two rollers, including effects of transport velocity and surrounding air. The paper web is modelled as a three-dimensional orthotropic structure. The influence of air is accounted for by utilizing fluid–solid interaction analyses based on acoustic theory. The contribution of transport velocity is included through gyroscopic matrices and forces. The structural response on harmonic excitations has been studied using linear and non-linear models. Results show that air significantly reduces eigenfrequencies of the web. So called “edge-flutter” is nothing but the result of skew tension profile. Excessive web vibration can be eliminated by adjusting the web tension.     

A strain-rate-dependent concrete material model for ADINA

The analysis, design and/or evaluation of protective structures and facilities for military use demands the accurate determination of material and structural response to high-intensity, short-duration impulse loadings. There currently exists a preponderance of data supporting increased strength characteristics in concrete, the primary construction material for protective facilities, at high strain rates. This paper summarizes the modification of the nonlinear concrete material model currently employed in the ADINA finite-element computer programs to account for high strain rate effects. The resultant strain-rate-dependent concrete material model encompasses the strain-rate range from 10⁻⁷s⁻¹ (quasi-static) to 10³s⁻¹, in both compression and tension.     

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.     

Inelastic behavior modelling of concrete in low and high strain rate dynamics

This work deals with response modeling of concrete for dynamic loading. As in statics one has to account for substantial difference of inelastic response in tension and compression, the anisotropy of the response induced by complex cracking patterns and the need of irreversible deformation due to frictional sliding or non-closing cracks. On the top of that, in dynamics, we also have to handle the hardening or softening phenomena which explain a particular hysteretic response for a given cyclic loading as well as the strain rate effects. The latter should further be addressed separately for high as opposed to low strain rates. The main goal of this work is to develop the concrete constitutive model capable of reproducing the salient features experimentally observed. We present one theoretical development for the constitutive model of concrete at low strain rates. The same kind of developments are then carried out for high strain dynamic behavior. Both chosen models belong to the class of coupled plasticity damage models briefly presented.     

Finite element analysis of reinforced and prestressed concrete structures including thermal loading

This paper describes the application of finite element techniques to the solution of nonlinear concrete problems. Reinforced concrete thick plates and shells are first considered for which both a perfect and strain-hardening plasticity approach are employed to model the compressive behaviour. A dual criterion for yielding and crushing in terms of stresses and strains is considered, which is complemented with a tension cut-off representation. Degenerate thick shell elements employing a layered discretisation through the thickness are adopted and both reduced and selectively integrated 8-node serendipity and heterosis elements are considered.Thermal loading of prestressed concrete structures is also considered which necessitates the inclusion of time effects in the analysis. The technique described in this paper involves concurrently solving an uncoupled set of equations within a time interval to provide both the displacement and temperature increments. A two-level time stepping scheme is employed to predict temperature changes within a time interval and elasto-viscoplastic material analysis is performed using an explicit forward-difference scheme incorporating an equilibrium iteration procedure. The constitutive model for the concrete is essentially identical to that employed for the plate and shell analysis.Numerical examples are presented for both types of analysis and comparison is made with experimental results whenever possible. Additionally, results for thermal loading are presented which indicate that a full transient thermal-mechanical analysis is sometimes essential in order to obtain a realistic structural response.     

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.     

混凝土板裂纹扩展的态型近场动力学模拟

构建考虑混凝土拉压异性和宏观断裂特征的混凝土类材料非局部态型近场动力学本构模型,并通过引入动态松弛、系统失衡判断和力边界等效等算法,构建适于分析混凝土类材料和结构变形破坏过程的态型近场动力学数值模拟体系.通过分组模拟和定量计算,分析算法的收敛性、计算精度和效率等问题;在此基础上开展含不同角度中心裂纹混凝土板的破坏模拟.     

An elasto-viscoplastic analysis of direct extrusion of a double base solid propellant

In this study, three-dimensional modelling of extrusion forming of a double base solid rocket propellant is performed on Ansys® finite element analysis program. Considering the contact effects and the time dependent viscous and plastic behaviour, the solid propellant is assumed to obey the large deformation elasto-viscoplastic material response during direct extrusion process. The deformed shape, hydrostatic pressure, contact stress, equivalent stress, total strain values are determined from the simulation in order to get insight into the mechanical extremity that the propellant has undergone during processing. Hydrostatic pressure and contact stress distributions have been found to be important parameters due to safety reasons of the nitro-glycerine content in the bulk of the propellant.     

Bifurcation in the numerical simulation of softening mechanisms

Non-linear simulation of strain-softening materials is often impeded by the presence of singular points encountered along the equilibrium path. Available numerical techniques aimed at the treatment of singular points are presented. Emphasis is placed on bifurcation analysis. Two numerical examples of structural bifurcation are presented. In the first example, a direct tension test on a notched concrete bar is simulated, displaying a symmetric bifurcation. In the second example, a direct tension test on a tapered concrete bar is simulated, displaying a non-symmetric bifurcation. The bifurcation analysis techniques introduced are shown to be effective. The need for systematic bifurcation analysis in the non-linear simulation of strain-softening materials is concluded.     

Simulation model for micromechanical angular rate sensor

A simulation model for an angular rate sensor, a gyroscope, is presented. The device is based on a micromechanical dual torsional mass system which is actuated electrostatically and sensed capacitively. Model equations describing a dynamic, non-linear system are first presented and then realized as an electrical equivalent circuit. The vibrational modes of the system are modelled with coupled resonator circuits. The electrostatic and Coriolis forces as well as variable capacitances in the small air gaps are modelled with non-linear controlled current sources. External forces, torques and electrical actuation can act as inputs to the device. The model presented allows numerical sensor simulations concurrently with the interfacing electronics in the time and frequency domains. The model is verified by comparing its simulation results to measured frequency responses and capacitance-voltage characteristics.     

An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model

Pure elastic damage models or pure elastic plastic constitutive laws are not totally satisfactory to describe the behaviour of concrete. They indeed fail to reproduce the unloading slopes during cyclic loading which define experimentally the value of the damage in the material. When coupled effects are considered, in particular in hydro-mechanical problems, the capability of numerical models to reproduce the unloading behaviour is essential, because an accurate value of the damage, which controls the material permeability, is needed. In the context of very large size calculations that are needed for 3D massive structures heavily reinforced and pre-stressed (such as containment vessels), constitutive relations ought also to be as simple as possible. Here an elastic plastic damage formulation is proposed to circumvent the disadvantages of pure plastic and pure damage approaches. It is based on an isotropic damage model combined with a hardening yield plastic surface in order to reach a compromise as far as simplicity is concerned. Three elementary tests are first considered for validation. A tension test, a cyclic compression test and triaxial tests illustrate the improvements achieved by the coupled law compared to a simple damage model (plastic strains, change of volumetric behaviour, decrease in the elastic slope under hydrostatic pressures). Finally, one structural application is also considered: a concrete column wrapped in a steel tube.     

Non-linearity measures for a class of SISO non-linear systems

A new measure of non-linearity, that is captured by two linear systems, is proposed to quantify the size of the non-linearity in the input/output behaviour of SISO non-linear systems. As such, the controller design for the non-linear system is simplified to the design of a controller for these two linear systems. It is also shown that when Hammerstein and Wiener models are involved, the controller design for these two structures are equivalent if the linear dynamic term is stable. Two examples, a numerical example and a non-linear system characterized by a time-delay and a variable gain are used to demonstrate these concepts.     

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.     

Hybrid-displacement (Trefftz) formulation for softening materials

This paper reports on the nonlinear static analysis of 2D concrete structures using a non-conventional finite element formulation. The nonlinear behavior of the material is modelled with a continuum non-local and isotropic damage model. While the material’s behavior is linear elastic, a pure hybrid-displacement Trefftz formulation is adopted. From the point where the concrete assumes a nonlinear behavior, this approach degenerates into a hybrid-displacement formulation. The computational performance is tested by means of two numerical examples which show that the proposed model predicts correctly the global behavior of the structures.     

Topology optimization of structures with anisotropic plastic materials using enhanced assumed strain elements

The focus of this paper is on consistent and accurate adjoint sensitivity analyses for structural topology optimization with anisotropic plastic materials under plane strain conditions. In order to avoid the locking issue, the Enhanced Assumed Strain (EAS) elements are adopted in the finite element discretization, and the anisotropic Hoffman plasticity model, which can simulate the strength differences in tension and compression, is incorporated within the framework of density-based topology optimization. The path-dependent sensitivity analysis is presented wherein the enhanced element parameters are consistently incorporated in the constraints. The objective of topology optimization is to maximize the plastic work. Several numerical examples are presented to show the effectiveness of the proposed framework. The results illustrate that the optimized topologies are highly dependent on the plastic anisotropic material properties.     

Computer analysis of impact behavior of concrete filled steel tube columns

This paper presents a numerical study of the response of axially loaded concrete filled steel tube (CFST) columns under lateral impact loading using explicit non-linear finite element techniques. The aims of this paper are to evaluate the vulnerability of existing columns to credible impact events as well as to contribute new information towards the safe design of such vulnerable columns. The model incorporates concrete confinement, strain rate effects of steel and concrete, contact between the steel tube and concrete and dynamic relaxation for pre-loading, which is a relatively recent method for applying a pre-loading in the explicit solver. The finite element model was first verified by comparing results with existing experimental results and then employed to conduct a parametric sensitivity analysis. The effects of various structural and load parameters on the impact response of the CFST column were evaluated to identify the key controlling factors. Overall, the major parameters which influence the impact response of the column are the steel tube thickness to diameter ratio, the slenderness ratio and the impact velocity. The findings of this study will enhance the current state of knowledge in this area and can serve as a benchmark reference for future analysis and design of CFST columns under lateral impact.