Ideal Plastic Model Research Articles

Analytical solution for the resistance of composite beams subjected to bending

The paper deals with the resistance of steel and concrete composite beams, named BH beams, subjected to bending. They are structurally connected with prefabricated or castin situslabs, forming floor slab system. The beams under consideration consist of the reinforced concrete (RC) rectangular core placed inside a reversed TT welded profile. The stress-strain relationship for concrete in compression of the RC core is assumed for nonlinear analysis according to Eurocode 2. For reinforcing and profile steels linear elastic – ideal plastic model is applied. The normalized ultimate bending moment determining the resistance of the BH beam is derived by integrating the equilibrium equations of the bending moments about the horizontal axis of the RC core rectangle, taking into account the physical and geometrical relationships. The presented model was verified by tests carried out on two BH beams subjected to bending. The comparisons made indicated good convergence between the analytical solution and the experimental results in ultimate bending moments.

Piles and lateral loads: comparison of calculation methods

Introduction. Calculation and analysis of pile resistance to loads remains to be a relevant problem in geoengineering. The design of pile foundations is currently performed using diverse analytical, empirical and numerical methods. However, the reliability of these methods remains to be a topic of interest among researchers and designers. This research paper analyses methods used for calculating the lateral-load capacity of piles in comparison with field-test data. Materials and methods. The paper dwells upon the development of reliable analytical expressions based on mathematical models of the pile–soil interaction. Main existing mathematical models of the soil environment, including the Mohr – Coulomb elastic ideal plastic model and the hardening soil model (HSM) were analysed. A particular attention was paid to a variety of factors affecting the pile–soil interaction, such as natural factors, pile types, pile sinking depth and technology, configurations of loads, as well as time-changed processes. A comparison of methods for calculating the lateral-load capacity of piles was conducted. To that end, calculations using the Mohr – Coulomb model and the local elastic strain theory (still required by building codes) were performed. High-level solid elements were used to develop and compute a finite-element pile-in-soil model in a spatial setting. Another model on the basis of parametric pile elements was designed using the MIDAS software. Results. It is established that the use of numerical calculation methods for evaluating the capacity and movements of pile foundations provides results comparable to those of field tests. These methods demonstrate a higher reliability compared to standardized analytical techniques. Conclusions. The reliability of numerical calculations of pile resistance to lateral impact is shown to be sufficiently high, thus being feasible for use in geoengineering. The use of these methods should be based on advanced non-linear soil models, such as HS, CamClay, etc.

Strips of localization of plastic deformation

Model of slip band propagation in materials with yielding plateau is introduced. Development of a slip band is modeled in a form of loss of stability during transition of the material from an elastic state to hardening. This transition is the generalization of crack mode I development model by Novozhilov (J Appl Math Mech 3:201–210, 1969) in elastic solids. Possibility for slip bands of limited length is shown in the model in contrast to ideal plasticity model that only leads to infinite slip bands. Problems of localization in a form of slip bands in a state for the pure shear and for intermaterial layer are considered. For different external loads and various mechanical properties of the interlayer, the lengths of the localization zone of plastic deformations, the graphs of the tangential displacement jump in this zone, and the shear stress on their continuation are found.

Mathematical model for the bending of plastically anisotropic beams

A mathematical model for the bending of a plastically anisotropic beam simply supported at both ends and subjected to a constant moment is considered. A differential equation with variable coefficients is derived for the beam curvature. The yield points of the beam material under tension and compression are assumed to be known. The elastoplastic bending of the beam with allowance for the strength-different (SD) effect is considered. The classical Bernoulli–Euler beam theory and the ideal plasticity model are used construct the mathematical model, and the problem is solved analytically. The solutions obtained for a classical isotropic beam and an SD beam are compared, and the contribution of the SD effect is analyzed. The problem is solved completely, and its results can be used to study bending under different loading.

Group analysis of an ideal plasticity model

A group analysis of a system describing an ideal plastic flow is made in order to obtain analytical solutions. The complete Lie algebra of point symmetries of this system are given. Two of the infinitesimal generators that span the Lie algebra are original to this paper. A classification into conjugacy classes of all one- and two-dimensional subalgebras is performed. Invariant and partially invariant solutions corresponding to certain conjugacy classes are obtained using the symmetry reduction method. Solutions of algebraic, trigonometric, inverse trigonometric and elliptic type are provided as illustrations and other solutions expressed in terms of one or two arbitrary functions have also been found. For some of these solutions, a physical interpretation allows one to determine the shape of feasible extrusion dies corresponding to these solutions. The corresponding tools could be used to curve rods or slabs, or to shape a ring in an ideal plastic material by an extrusion process.

Deformation and fracture of a material in one-dimensional elastoplastic problems

The ideal plasticity model based on the Tresca-Saint-Venant criterion is used to solve one-dimensional problems of deformation and fracture of solids with circular boundaries. A thickwalled cylinder and a hollow sphere under pressure, cylindrical and hollow cavities in an unbounded body, and uniform extension at infinity of a plate with a free circular hole are considered. In simple elastoplastic problems, the proposed approach allows one to determine the value of the maximum external load at the fracture initiation and the motion of the fracture front for a given displacement of points of the contour on which this load acts.

A geometrical and physical nonlinear finite element model for spatial thin-walled beams with arbitrary section

Based on the theories of Bernoulli-Euler beams and Vlasov’s thin-walled members, a new geometrical and physical nonlinear beam element model is developed by applying an interior node in the element and independent interpolations on bending angles and warp, in which factors such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and second shear stress are all considered. Thereafter, geometrical nonlinear strain in total Lagarange (TL) and the corresponding stiffness matrix are formulated. Ideal plastic model is applied to physical nonlinearity to comply with the yield rule of Von Mises and incremental relationship of Prandtle-Reuss. Elastoplastic stiffness matrix is derived by numerical integration on the basis of the finite segment method. Examples show that the developed model is feasible in analysis of thin-walled structures with high accuracy.

Thermal fatigue behavior of an iron-based laser sintered material

Direct metal laser sintering is a rapid manufacturing technique to make intricate and near net-shaped parts. An iron-based laser sintered metal was studied to evaluate its thermal fatigue properties. The test was performed using cylindrical specimens in a high power induction heating system equipped with a laser strain gauge for a contactless surface strain measurement. Initiation of thermal fatigue cracks occurred preferentially at pores and layer interfaces, while propagation of cracks followed along phase boundaries and thin inter-dendritic phases and showed an inter-granular fracture. By using the fundamental Fourier equation for heat conduction, the temperature cycle was modeled and calculated. A thermo elastic ideal plastic model was used to deduce the thermal stress based on surface strain experimentally measured. Finally, the temperature distribution, thermal stresses and mechanical strains were discussed with respect to thermal fatigue damage.

Application of the slip-line field method to the analysis of die cavity filling

The article concerns the selected problems of closed-die forging. It is focused on the analysis of use the slip-line field method in flash design process. The new slip-line field elemental technique (SLFET) has been presented in this paper, too.The theoretical analysis is compared with the forging simulations made in the finite element method (FEM). As a tools were used the closed-dies with a flat parallel flash land. It assured extrusion process (parts with the boss) in plane strain conditions.Application of the slip-line field method permits to compute a load and efficient filling of die cavity (maximal height of the boss). An ideal plastic model of material has been utilized on the analysis. This work presents influences among flash land geometrical parameters on degree of die cavity filling and load. The poly-optimization of flash land parameters has been presented in here, too. Based on obtained conclusions, authors have worked out a computer program, which implements a new SLFET method.

Application of the slip-line field method to the analysis of die cavity filling

The article concerns the selected problems of closed-die forging. It is focused on the analysis of use the slip-line field method in flash design process. The new slip-line field elemental technique (SLFET) has been presented in this paper, too. The theoretical analysis is compared with the forging simulations made in the finite element method (FEM). As a tools were used the closed-dies with a flat parallel flash land. It assured extrusion process (parts with the boss) in plane strain conditions. Application of the slip-line field method permits to compute a load and efficient filling of die cavity (maximal height of the boss). An ideal plastic model of material has been utilized on the analysis. This work presents influences among flash land geometrical parameters on degree of die cavity filling and load. The poly-optimization of flash land parameters has been presented in here, too. Based on obtained conclusions, authors have worked out a computer program, which implements a new SLFET method.

Limit analysis of cracked structures by mathematical programming and finite element technique

Limit analysis of cracked structures using mathematical programming and finite element method is presented. This direct algorithm is based on a proposition of the modified Markov variational principle. The obtained upper bound formula is applicable with any kinematic admissible finite elements. The regularization of plastic dissipation function is performed to overcome the indetermination of the objective gradient in the rigid region and to realize a smooth transition of the objective function between the plastified and non-plastified regions. In order to simulate the singularity of crack-tip strain field for an ideal plastic model, the separate-point degenerated finite elements are used around the crack tips. This improves the precision of limit solutions. Numerical results of plane and axisymmetric cracked structures are extensively compared with analytic ones. The application of limit analysis in fracture mechanics is illustrated by an example.

Deformation of a flowing powder with nonviscous friction

A model for an ideally plastic body is extended to a powder medium with nonorthogonal slip lines; it is shown that some properties of the ideal-plasticity model are not essential and should not be generalized, namely, the coincidence between the characteristics for the velocity and stress distributions, and independence of the velocity distribution from the possible differences in the shears on the areas, A closed system of equations is derived, and the properties of the discontinuous solutions are discussed; boundary-value problems are formulated. It is shown that the stability-loss lines are arcs of circles (surface of a circular cylinder) in the case of bank stability.