DESIGN OPTIMIZATION FOR TRUSS STRUCTURES UNDER ELASTO-PLASTIC LOADING CONDITION

In this paper, a method for the design optimization of elasto-plastic truss structures is proposed based on parametric variational principles （PVPs）. The optimization aims to find the minimum weight/volume solution under the constraints of allowable node displacements. The design optimization is a formulation of mathematical programming with equilibrium constraints （MPECs）. To overcome the numerical difficulties of the complementary constraints in optimization, an iteration process, comprising a quadratic programming （QP） and an updating process, is employed as the optimization method. Furthermore, the elasto-plastic buckling of truss mem- bers is considered as a constraint in design optimization. A combinational optimization strategy is proposed for the displacement constraints and the buckling constraint, which comprises the method mentioned above and an optimal criterion. Three numerical examples are presented to show the validity of the methods proposed.

Elasto-plastic postbuckling of damaged orthotropic plates

Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.

Dynamic Buckling of Elasto-Plastic Cylindrical Shells Under Axial Fluid-Solid Impact Load

The dynamic buckling of elasto-plastic cylindrical shells under axial fluid-solid impact is investigated theoretically. A simplified liquid- gas- structure model is given to approximately imitate the problem. The basic equation of the structure is derived from a minimum principle in dynamics of elasto-plastic continua at finite deformation, and the flow theory of plasticity is employed. The liquid is incompressible and the gas is compressed adiabatically. A number of numerical results are presented and the characteristics of the buckling behavior under fluid-solid impact are illustrated.

Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.

TIME DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR DYNAMIC ANALYSES IN SATURATED PORO-ELASTO-PLASTIC MEDIUM

A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed.As compared with the existing discontinuous Galerkin finite element methods,the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured,whereas the discontinuity of the velocity vector at the discrete time levels still remains.The computational cost is then obviously reduced, particularly,for material non-linear problems.Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed.Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.

NONLINEAR AND ELASTO-PLASTICITY CONSOLIDATION MODELS OF UNSATURATED SOIL AND APPLICATIONS

The non-linear constitutive model suggested by the authors and the Alonso's elasto-plasticity model of unsaturated soil modified by the authors are introduced into the consolidation theory of unsaturated soil proposed by CHEN Zheng-han, and the non-linear and the elasto-plasticity consolidation models of unsaturated soil are obtained. Programs related to the two consolidation models are designed, and a 2-D consolidation problem of unsaturated sail is solved using the programs, the consolidation process and the development of plastic;one under multi-grade bad are studied. The above research develops the consolidation theory of unsaturated soil to a new level.

Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.

ELASTO-PLASTICITY ANALYSIS BASED ON COLLOCATION WITH THE MOVING LEAST SQUARE METHOD

A meshless approach based on the moving least square method is developed for elasto-plasticity analysis,in which the incremental formulation is used.In this approach,the dis- placement shape functions are constructed by using the moving least square approximation,and the discrete governing equations for elasto-plastic material are constructed with the direct collo- cation method.The boundary conditions are also imposed by collocation.The method established is a truly meshless one,as it does not need any mesh,either for the purpose of interpolation of the solution variables,or for the purpose of construction of the discrete equations.It is simply formu- lated and very efficient,and no post-processing procedure is required to compute the derivatives of the unknown variables,since the solution from this method based on the moving least square approximation is already smooth enough.Numerical examples are given to verify the accuracy of the meshless method proposed for elasto-plasticity analysis.

EFFECTIVE NUMERICAL METHODS FOR ELASTO-PLASTIC CONTACT PROBLEMS WITH FRICTION

Several effective numerical methods for solving the elasto-plastic contact problems with friction are pres- ented.First,a direct substitution method is employed to impose the contact constraint conditions on condensed finite ele- ment equations,thus resulting in a reduction by half in the dimension of final governing equations.Second,an algorithm composed of contact condition probes and elasto-plastic iterations is utilized to solve the governing equation,which distinguishes two kinds of nonlinearities,and makes the solution unique.In addition,Positive-Negative Sequence Modifica- tion Method is used to condense the finite element equations of each substructure and an analytical integration is intro- duced to determine the elasto-plastic status after each time step or each iteration,hence the computational efficiency is en- hanced to a great extent.Finally,several test and practical examples are pressented showing the validity and versatility of these methods and algorithms.

A STUDY ON THE EFFECT OF RADIAL INERTIA ON THE ELASTO-PLASTIC COMBINED STRESS WAVE PROPAGATION IN THIN-WALLED TUBES

An in-depth analysis of propagation characteristics ofelasto-plastic combined stress waves in circular thin-walled tubeshas been made. In obtaining the simple-wave solution, however, mostresearches have ignored the influence of the circumferential stressrelated to the radial inertial ef- fect in the tubes. In this paperthe incremental elasto-plastic constitutive relations which areconve- nient for dynamic numerical analysis are adopted, and thefinite-difference method is used to study the evolution adpropagation of elasto-plastic combined stress waves in a thin-walledtube with the radial inertial effect of the tube considered. Thecalculation results are compared with those obtained when the radialinertial effect is not considered. The calculation results show thatthe radial inertial effect of a tube has a fairly great influence onthe propagation of elasto-plastic combined stress waves.

An elasto-plastic constitutive model of moderate sandy clay based on BC-RBFNN

Application research of neural networks to geotechnical engineering has become a hotspot nowadays.General model may not reach the predicting precision in practical application due to different characteristics in different fields.In allusion to this,an elasto-plastic constitutive model based on clustering radial basis function neural network(BC-RBFNN) was proposed for moderate sandy clay according to its properties.Firstly,knowledge base was established on triaxial compression testing data;then the model was trained,learned and emulated using knowledge base;finally,predicting results of the BC-RBFNN model were compared and analyzed with those of other intelligent model.The results show that the BC-RBFNN model can alter the training and learning velocity and improve the predicting precision,which provides possibility for engineering practice on demanding high precision.

Analytic Solution of Elasto-Plastic Stress in Infinite Slope under Uniform Load

According to the Mohr-Coulomb yield criterion, the stress field of the infinite slope is derived under a vertical uniform load q on the top of the slope. It is indicated that elastic and elasto-plastic states would occur in the slope. When q is smaller than the critical load, q(p), the slope is in the elastic state. If q equals q(p), the slope is in the critical state, and the plastic deformation would occur along the critical angle. With the increase of q, the plastic zone would extend, and the slope is in the elasto-plastic State. If q equals limit load, the slope is in the limit equilibrium state. The slope may be divided into three zones. Some charts of the critical angle, the critical and limit load coefficients are presented in this paper.

Contact dynamics of elasto-plastic thin beams simulated via absolute nodal coordinate formulation

Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation（ANCF）. The internal force of the elasto-plastic spatial thin beam element is derived under the assumption that the plastic strain of the beam element depends only on its longitudinal deformation.A new body-fixed local coordinate system is introduced into the spatial thin beam element of ANCF for efficient contact detection in the contact dynamics simulation. The linear isotropic hardening constitutive law is used to describe the elasto-plastic deformation of beam material, and the classical return mapping algorithm is adopted to evaluate the plastic strains. A multi-zone contact approach of thin beams previously proposed by the authors is also introduced to detect the multiple contact zones of beams accurately, and the penalty method is used to compute the normal contact force of thin beams in contact. Four numerical examples are given to demonstrate the applicability and effectiveness of the proposed elasto-plastic spatial thin beam element of ANCF for flexible multibody system dynamics.

An elasto-plastic and viscoplastic damage constitutive model for dilatancy and fracturing behavior of soft rock squeezing deformation

Soft rock squeezing deformation mainly consists of pre-peak damage-dilatancy and post-peak fracture-bulking at the excavation unloading instant,and creep-dilatancy caused by time-dependent damage and fracturing.Based on the classic elastoplastic and Perzyna over-stress viscoplastic theories,as well as triaxial unloading confining pressure test and triaxial unloading creep test results,an elastoplastic and viscoplastic damage constitutive model is established for the short-and long-term dilatancy and fracturing behavior of soft rock squeezing deformation.Firstly,the criteria for each deformation and failure stage are expressed as a linear function of confining pressure.Secondly,the total damage evolution equation considering time-dependent damage is proposed,including the initial damage produced at the excavation instant,in which the damage variable increases exponentially with the lateral strain,and creep damage.Thirdly,a transient five-stages elasto-plastic constitutive equation for the short-term deformation after excavation that comprised of elasticity,pre-peak damage-dilatancy,post-peak brittle-drop,linear strain-softening,and residual perfectly-plastic regimes is developed based on incremental elasto-plastic theory and the nonassociated flow rule.Fourthly,regarding the timedependent properties of soft rock,based on the Perzyna viscoplastic over-stress theory,a viscoplastic damage model is set up to capture creep damage and dilatancy behavior.Viscoplastic strain is produced when the stress exceeds the initial static yield surface fs;the distance between the static yield surface fs and the dynamic yield surface fd determines the viscoplastic strain rate.Finally,the established constitutive model is numerically implemented and field applied to the-848 m belt conveyer haulage roadway of Huainan Panyidong Coal Mine.Laboratory test results and in-situ monitoring results validate the rationality of the established constitutive model.The presented model takes both the transient and time-dependent damage and fracturing into consideration.

Elasto-plastic analysis of masonry with anisotropic plastic material model

This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill's yield criterion and the Rankine's yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.

Settlement Analysis for An Embankment Considering Visco-Elasto-Plastic Characteristics

In the paper. a visco-elasto plastic constitutive model and a method for determining model parameters for soft clay are presented. In this model total strain of soft clay is assumed to be divided into three parts: instantaneous elastic, visco-elastic and visco-plastic. The characteristics of instantaneous and visco-elastic deformation of soft clay are simulated by Merchant's model, the plastic is by a model with two yield surfaces. And related constitutive equation is conducted. A number of stress-controlled triaxial tests are performed to calculated the model parameters. The visco-elasto-plastic model is used for analysis of the displacement of an embankment on soft ground by use of three-dimensional finite element method. The predicted settlements agree well with the measured data. It is indicated that the viscous characteristics should be taken into account in deformation analysis for soft clay.

ANALYSIS ON THERMAL ELASTO-PLASTIC ASPERITY CONTACTS OF LAYERED MEDIA

A thermal elasto-plastic asperity contact model is investigated, which takes into account the steady-state heat transfer and the asperity distortion due to thermal elasto-plastic deformations. A hard coating and a soft coating are applied to study the correlations between contact area and contact pressure, average gap and contact pressure, coating thickness and contours of the contact stress distribution, etc. The effects of material properties, coating thickness, frictional coefficient, and the heat input combinations on the stress distribution are investigated and discussed. The frictional heat input increases the maximum value of yon Mises stress. Finally, the appropriate thickness of the hard coating is also discussed. To protect the substrate, one can choose hard coating and the thickness of that is suggested that can be hc=70 Rm.

STATIONARY DISCONTINUITY AND FLUTTER INSTABILITY OF WAVE PROPAGATION IN ELASTO-PLASTIC SATURATED POROUS MEDIA

In the present work a model based on the Biot theory for simulating coupled hydrodynamic behavior mi saturated porous media is utilized with integration of the inertial coupling effect between the solid-fluid phases of the media into the model. The non-associated Drucker-Prager criterion to describe nonlinear constitutive behavior of pressure dependent elasto-plasticity for the media is particularly considered. With no consideration of compressibility of solid grains and the pore fluid, the discontinuity and instability of the wave propagation in saturated porous media axe analyzed for the plane strain problems in detail. The critical conditions of stationary discontinuity and flutter instability in the wave propagation are given. The results and conclusions obtained by the present work will provide some bases or clues for overcoming the difficulties in numerical modeling of wave propagation in the media subjected to dynamic loading.

Elasto-Plastic FEM Analysis of Residual Stress in Spun Tube

The residual stress distribution of Hastelloy C corrosion-resistant alloy tubes after power spinning was simulated with the elasto-plastic finite element method combining with the element birth and death technique, the influences of spinning parameters on the distribution of the residual stress were investigated in detail, and the formation mechanism of residual stress during tube spinning was discussed. Based on the calculation of the residual stress, the reasons for annealing cracks on the spun tube during interpass heat treatment were explored. The simulation results and the characteristics of annealing cracks show that the circumferential residual tensile stress is a main factor to cause the annealing cracks.