Elastoplastic 3D Deformation and Stress Analysis of Strip Rolling

An elastoplastic method for analyzing the 3D deformation, stress and transverse distribution of tension stress during cold strip rolling is developed. The analysis is based on the elastoplastic variational principle in which a kinematically admissible velocity field is constructed with the lateral flow function as an unknown function. The stress distribution and volume strain distribution are obtained by solving the simultaneous equations formed by the longitudinal differential equation of equilibrium and constitutive equations. The lateral flow function is determined by minimizing the total energy dissipation rate. Experimental investigation was carried out on a reversible cold mill. The front tension stress distributions in cold rolled strips were measured by a multi roll segmented tension sensing shapemeter. The calculated results are in good agreement with the measured ones.

Elastoplastic analysis of knee bracing frame

The knee bracing steel frame (KBF) is a new kind of energy dissipating frame, which combines excellent ductility and lateral stiffness. As the structural fuse of the frame, the knee element will yield first during a severe earthquake so that no damage occurs to the major structural members and the rehabilitation is easy and economical. To help fully understand the relations be- tween its seismic performance and the structural parameters, systematic elastoplastic analysis of the KBF structure with finite element method was conducted in this work. Finally, general design recommendations were made according to the results of the analysis.

FUNDAMENTAL OF DYNAMICAL ANALYSIS OF THE BLAST-RESISTANT UNDERGROUND STRUCTURES

In this paper, the generalized variational principle of dynamic analysis for the blast-resistant underground structures is established, and the corresponding generalized functional of elastoplastic analysis for underground structures is derived, and the generalized variational principle of nonconservative system is given, thus the fundamental of dynamical analysis for underground structures to resist blast is proposed. Finally, for the underground cylindrical structure to resist blast, dynamical calculations are made, and compared with the test results.

A note on a family of proximal gradient methods for quasi-static incremental problems in elastoplastic analysis

Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity.However,in literature these algorithms are described individually for specific yield criteria,and hence there exists no guide for application of the algorithms to other yield criteria.This short paper presents a general form of algorithm design,independent of specific forms of yield criteria,that unifies the existing proximal gradient methods.Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.

Elastoplastic Analysis of Circular Tunnel in Saturated Ground Under Different Load Conditions

When a tunnel is excavated below the groundwater table,groundwater flows in through the excavated wall of the tunnel and seepage forces act on it.These forces significantly affect the ground reaction curve,which is defined as the relationship between the internal pressure and radial displacement of the tunnel wall.This study investigates analytical solutions for seepage forces acting on the lining of a circular tunnel under steady-state groundwater flow.Considering the tunnel’s construction or service period and boundary conditions,the direction of maximum principal stress changes,and the input stress of the Mohr-Coulomb criterion varies.The stress distribution and yield range of the surrounding soils and linings are studied.The first,second,and third critical inner pressures are defined and evaluated.The influence of the seepage field on the plastic radius,first critical pressure,and stress distribution of the tunnel is analyzed.It is shown that during the construction period,the seepage force promotes the expansion of the yield area,whereas during the service period,the opposite is the case.The first critical pressure increases nearly linearly with the distant water pressure.The radial stress distribution decreases clearly in comparison with that when the seepage force is not considered,and the reduction is more prominent when internal pressure increases.The tangential stress distribution increases clearly compared with that when the seepage force is not considered.

Elastoplastical analysis on cylinder of different moduli in tension and compression

The constitutive equation was deduced. The results were obtained from theelastic and elastoplastical analysis of the cylinder sample applied with different ratios ofload on both the inner and outer sides and different moduli ratio. The factors affecting thedevelopment of the plastic field of the cylinder with finite radius were shown. The resultsshow that the different moduli ratio is the most important factor in the development of theplastic zone. The slight fluctuation of the ratio will bring multiplied increment of the displacement, which may result in the final destruction of the engineering material.

ELASTOPLASTIC ANALYSIS OF THICK-WALLCYLINDER CONSIDERING THE MATERIAL'S DILATANCY CHARACTER

Impermeable bentonite or its mixtures have been proposed as candidate materials to be used in the geotechnical disposal of radioactive nuclear waste. These materials are filled in the space between a canister containing radioactive nuclear waste and an underground chamber to absorb the radionuclide emitting from the canister and simultaneously retard its migration accompanying the perrneation of underground water to prevent the surrounding environment from po1lution. On the basis of the established elastoplastic strain-hardening mechanical model considering the material’s dilatancy character,the authors carry out the stress-strain analysis of a thick-wa1l cylinder in a plane strain state subJected to a pressure difference between internal and external pressures. The analysis may be expected to be a theoretical basis for developing a coupled shear and permeability test apparatus for conducting a permeability test along a sheared plane in a specimen. The apparatus will be used to study the effects of shear strain on the variation of geotechnical materials’ permeability coefficient in order to evaluate the influence of shear strain caused by nonuniform deformation and/or earthquake on the long-term safety of the disposal system of radioactive nuclear waste. The theoretlcal analysls methods in this paper can be directly spread to the analysis of the deformation and stability of tunnels or roadways driven in soft soils or high moisture-bearing soft rocks.

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.

A study on boundary integral equations for dynamic elastoplastic analysis for the plane problem by TD-BEM

The equivalent stress fundamental solution for the elastoplastic dynamic plane strain problem is proposed to transform the virtual work in the third direction to the plane.Subsequently,based on Betti reciprocal theorem,by adopting the time dependent fundamental solutions in terms of displacement,traction and equivalent stress,the boundary integral equations for dynamic elastoplastic analysis for the plane strain problem are established.The establishment procedures for the displacement and the stress boundary integral equations,together with the stress equation at boundary points,are presented in details,while the standard discretization both in time and space under the frame of time domain boundary element method(TD-BEM)and the solution of the algebraic equations are also briefly stated.Two verification examples are presented from different viewpoints,for elastic and elastoplastic analysis,for 1-D and 2-D geometries,and for finite and infinite domains.The TD-BEM formulation for dynamic elastoplastic analysis is presented for the plane strain problem as an example,where the formulation is also applicable for the plane stress problem by properly transforming the elastic constants and adopting the corresponding fundamental solutions.