Elasto-plastic Stability Research Articles

Global stability design of double corrugated steel plate shear walls under combined shear and compression loads

As a novel structural component, the Double Corrugated Steel Plate Shear Wall (DCSPSW) is formed by interlocking two corrugated steel plates using high-strength bolts. This paper investigates the global stability design methods for DCSPSWs under combined shear and compression loads. Firstly, this paper examines the elastic buckling performance of DCSPSWs under horizontal shear loads and vertical compression loads separately. A bolt spacing factor (η) is introduced to reflect the influence of bolt spacing on the elastic buckling stress of DCSPSWs. Then, based on extensive finite element analysis (FEA), this paper investigates the elastoplastic buckling behavior of DCSPSWs under shear loads and compression loads and establishes the corresponding stability curves to predict ultimate load-bearing capacity. It is found that the stability coefficients (φs and φc) are closely related to the normalized slenderness ratios (λns and λnc). A smaller bolt spacing allows the DCSPSWs to exhibit improved elastic and elastoplastic stability. Finally, this study investigates the load-bearing performance of DCSPSWs under combined shear and compression loads and proposes the design formulas. The results show that the correlation curve of N/Nu-V/Vu can provide a conservative and accurate design. The research findings of this paper are advantageous for promoting the application of the innovative DCSPSWs.

Out-of-Plane Stability Analysis of the Circular Box Arch with Sinusoidal Corrugated Webs

This paper presents an arch structure called the circular box arch with sinusoidal corrugated webs (CBASCW). This study investigates the out-of-plane elastic buckling behavior and elastoplastic stability capacity of the arch through a combined approach of theoretical derivation and finite element simulation. The section stiffness of the arch, including flexural stiffness, shear stiffness, and torsional stiffness, is achieved through theoretical derivation. Additionally, the elastic buckling load in both pure compression and pure bending states is derived. A simplified model is also introduced, which can conveniently simulate the internal force and deformation of the arch. The elastoplastic instability mechanism and failure mode are studied under various loading conditions, including uniform radial load, end bending moment, vertical load uniformly distributed in full-span, and vertical load uniformly distributed in half-span. Furthermore, the stability curves of the arch under conditions of pure compression and pure bending are graphed by incorporating stability coefficient and regularized slenderness ratio. According to the simulation results obtained from the simplified model and the analysis of stability curves, a design formula for stability capacity is proposed.

Seismic safety evaluation method based on fiber-element strain for square-section steel piers

Inconsistency and incompatibility exist between the seismic capacity values obtained from shell-element models and the seismic demand results obtained from beam-based models in engineering. In this paper, the improved fiber model which can consider local instability of steel plates is used uniformly to conduct seismic capacity and seismic demand analyses under bidirectional earthquake actions. First, the restoring-force interaction curves of square-section steel piers are obtained under horizontal unidirectional and oblique loading; however, the evaluation method based on the restoring-force interaction curves may produce incorrect evaluation results according to the elastoplastic stability theory. Therefore, a new seismic safety evaluation method, based on the fiber-element strain within the effective damaged length (Led), is further proposed through the quasistatic analysis under the square spiral loading path. Dynamic seismic response analysis is conducted to verify the effectiveness of the proposed strain-based evaluation method. The results show that the ultimate state according to the compressive strain limit obtained via the square spiral loading is consistent with that based on the elastoplastic stability theory under bidirectional earthquake actions. The proposed method can not only coordinate the demand and capacity results, but also avoid misjudgment cases and facilitate engineering application.

Structural Stability Analysis of Eye of the Yellow Sea, a Large-Span Arched Pedestrian Bridge

To date, scholars’ research on the stability behavior of the arch structure mainly focuses on solid–web section arches, steel tubular truss arches and concrete-filled steel tubular arches, but the stability behavior of the novel spatial grid arch structure, which integrates the characteristics of grid structure and arch structure, is not yet clear. Based on the Eye of the Yellow Sea pedestrian bridge project in Rizhao, China, the stability behavior of this large-span spatial grid arch structure was studied, in this paper, by the project’s structure design team. The project is a glass covered steel arch pedestrian bridge with a span of 177 m, a height of 63.5 m, an elliptical section with a long axis of 18 m, and a short axis of 13.5 m. The elastic and the nonlinear elasto-plastic stability behavior considering different initial geometric imperfections, was analyzed by the ABAQUS finite element model. The buckling modes and the full-range load-displacement curve of the structure were analyzed, and the stress distribution, deformation mode and overall structural performance during the whole loading process were analyzed. The effects of initial imperfections, geometric nonlinearity and material nonlinearity on the ultimate load-carrying capacity of the structure were studied. The stability behavior of large-span spatial grid arch structure was studied in this paper, which provides an important reference for the design and analysis of such structures.

Elastoplastic buckling of a cylindrical shell with initial geometric imperfections and an elastic filler at external pressure

A technique has been developed for the numerical calculation of deformation and elastoplastic stability loss nonlinear problems rotating shells based on the Tymoshenko hypotheses for nonshallow shells taking into account geometric nonlinearities. Kinematic relations are formulated in velocities and constructed in the current status metric taking into account large deformations, displacements and rotation angles of shell elements. plastic flow theory with nonlinear isotropic hardening describes physical relations. The motion equations result from the virtual working power balance. Winkler foundation models the revolution shell and the elastic filler contact interaction. The numerical calculation is based on an explicit “cross” type mesh scheme. The dependence of the elastoplastic revolution shell stability loss form and the load critical value on the filler stiffness under various values of the initial imperfections amplitude was studied.

Investigation on Simulation Methods of Initial Geometric Imperfection Distribution in Elasto-plastic Stability Analysis of Single-layer Reticulated Shells

Based on the theory of probability and mathematical statistics and on the results of nearly 2000 cases of elasto-plastic stability analysis for single-layer reticulated shells, a new simulation method of initial geometric imperfection distribution, N-order eigenmode imperfection method, is developed. The elasto-plastic stability analyses of four types of commonly used single-layer reticulated domes were conducted with the random imperfection mode method, the eigenmode imperfection method and the N-order eigenmode imperfection method, respectively, by means of ANSYS. The results show that, though the random imperfection mode method can simulate the initial geometric imperfection distribution realistically, the calculation cost of this method is too large to popularize in design practice. Adopting the first order eigenmode to simulate the distribution of initial geometric imperfection may fail to derive the most unfavorable buckling load. The reliability of buckling load obtained from the eigenmode imperfection method cannot be guaranteed effectively. The N-order eigenmode imperfection method can evaluate the influence of initial geometric imperfection on structural stability reasonably, and capture the buckling load satisfying the requirement of the ‘3σ’ principle with less calculation. This method is a convenient and efficient way for designers to estimate stability performance of single-layer reticulated shells accurately and safely.

Elastoplastic Stability and Failure Analysis of FGM Plate with Temperature Dependent Material Properties under Thermomechanical Loading

THE PRESENT PAPER EXPLORES THE STABILITY AND FAILURE RESPONSE OF ELASTOPLASTIC NI/AL2O3 FUNCTIONALLY GRADED PLATE UNDER THERMOMECHANICAL LOAD USING NON-LINEAR FINITE ELEMENT FORMULATION BASED ON FIRST-ORDER SHEAR DEFORMATION THEORY AND VON-KARMAN’S NONLINEAR KINEMATICS. THE TEMPERATURE DEPENDENT THERMOELASTIC MATERIAL PROPERTIES OF FGM PLATE ARE VARIED IN THE THICKNESS DIREC-TION BY CONTROLLING THE VOLUME FRACTION OF THE CONSTITUENT MATERIALS (I.E., CERAMIC AND METAL) WITH A POWER LAW, AND MORI-TANAKA HOMOGENIZATION SCHEME IS APPLIED TO EVALUATE THE PROPERTIES AT A PARTICULAR THICKNESS COORDINATE OF FGM PLATE. THE ELASTOPLASTIC BEHAVIOR OF FGM PLATE IS ASSUMED TO FOLLOW J2-PLASTICITY WITH ISOTROPIC HARDENING, WHEREIN THE CERAMIC PHASE IS CONSIDERED TO BE ELASTIC WHEREAS THE METAL IS ASSUMED TO BE ELASTIC-PLASTIC IN ACCORDANCE WITH THE TAMURA-TOMOTA-OZAWA MODEL. NUMERICAL STUDIES ARE CONDUCTED TO EXAMINE THE EFFECTS OF MATERIAL AND GEOMETRICAL PARAMETERS, VIZ. MATERIAL IN-HOMOGENEITY, SLENDERNESS AND ASPECT RATIOS ON THE ELASTOPLASTIC BUCKING AND POSTBUCKLING BEHAVIOR AND THE FAILURE RESPONSE OF FGM PLATE. IT IS REVEALED THAT MATERIAL GRADATION AFFECTS THE STABILITY AND FAILURE BEHAVIOR OF FGM PLATE CONSIDERABLY. FURTHERMORE, IT IS ALSO CONCLUDED THAT FGM PLATE WITH ELASTIC MATERIAL PROPERTIES EXHIBITS ONLY STABLE EQUILIBRIUM PATH, WHEREAS THE ELASTOPLASTIC FGM PLATE SHOWS DESTABILIZING RESPONSE AFTER THE ULTIMATE FAILURE POINT.

Elasto-plastic stability of single-layer reticulated shells with aluminium alloy gusset joints

The single-layer reticulated shell with aluminium alloy gusset (AAG) joints is an innovative space structure system, and has been widely used in the building engineering. According to the bending behaviour of AAG joints obtained from the theoretical formulae, the finite element (FE) models of K6 AAG joint shells were established in the ANSYS program. The buckling performance of K6 shells with semi-rigid and rigid joints was discussed. It is indicated that the semi-rigid behaviour of AAG joints had a significant effect on the buckling performance of K6 shells. To develop a further understanding, parametric studies were performed, varying the span-to-thickness ratio, height-to-span ratio, ring, member section, joint bending behaviour, joint stiffness model, material property, load distribution, support condition and initial geometric imperfection. It is found that the effects of these parameters on the elasto-plastic stability of K6 shells with rigid and AAG joints were different obviously. At last, to predict the elasto-plastic buckling load of AAG joint shells, theoretical formulae were proposed on the basis of the FE results of more than 8000 shell models.

Nonlinear stability analysis of the frame structures

In this paper the phenomenon of instability of frames in elasto-plastic domain was investigated. Numerical analysis was performed by the finite element method. Stiffness matrices were derived using the trigonometric shape functions related to exact solution of the differential equation of bending according to the second order theory. When the buckling of structure occurs in plastic domain, it is necessary to replace the constant modulus of elasticity E with the tangent modulus Et. Tangent modulus is stress dependent function and takes into account the changes of the member stiffness in the inelastic range. For the purposes of numerical investigation in this analysis, part of the computer program ALIN was created in a way that this program now can be used for elastic and elasto-plastic stability analysis of frame structures. This program is developed in the C++ programming language. Using this program, it is possible to calculate the critical load of frames in the elastic and inelastic domain. In this analysis, the algorithm for the calculation of buckling lengths of compressed columns of the frames was also established. The algorithm is based on the calculation of the global stability analysis of frame structures. Results obtained using this algorithm were compared with the approximate solutions from the European (EC3) and national (JUS) standards for the steel structures. By the given procedure in this paper it is possible to follow the behavior of the plane frames in plastic domain and to calculate the real critical load in that domain.

Quantitative assessment of functional stability of forest ecosystems

Two hierarchical levels of forest ecosystem stability are distinguished: the labile phytocenotic level and the inertial soil-biotic level. For each level, indices of resistant and elastoplastic stability of biogeocenoses and forest formations have been calculated, and statistically significant equations for the relationships of these indices with environmental factors have been constructed. The relative contribution of each considered metabolic factor to a given index has been evaluated quantitatively, with verification of the calculation models.

Research on the Nonlinear Stability of the Steel Spatial Arch Truss with 120m Span and 0.2 Rise-Span Ratio

The elasto-plastic stability analysis on the steel spatial arch truss with 120m span and 0.2 rise-span ratio is carried out with the finite element program ANSYS. In the analyses, two conditions which are the geometric and material nonlinear, double nonlinear under different initial geometric defects are considered. The results show that the instability modes of arch trusses are all asymmetric instability of plane, and that the buckling load and plastic development of the four arch trusses with L/500, L/400, L/300 and L/200 initial geometric defects are decreased with the increase of different initial geometric defects, and that the axial stress of all web members is about the same, but the value of which does not exceed 235Mpa.

Analysis of overall stability bearing capacity of single-layer shell structures under high temperature condition

Based upon nonlinear analysis theories for single-layer reticulated shells under fire conditions, more than 800 FEA models for four types of single-layer reticulated shells (K8, Geodesic, Schwedler, and Lamella) with different geometric parameters were set, and nonlinear finite element complete-process analysis under fire condition were conducted on the two typical cases, i.e., global non-uniform temperature distribution and localized high temperature. By analyzing the calculation results for elasto-plastic stability bearing capacity, the practical calculation formulae for calculating elasto-plastic stability bearing capacity under fire condition were obtained.

The Research on the Nonlinear Stability of the Steel Spatial Arch Truss with 120m

In this paper, the elastic stability and elasto-plastic stability analysis on the steel spatial arch truss with 120m span and 0.2 rise-span ratio is carried out with the finite element program ANSYS. In the analyses, three conditions which are the geometric ,the geometric and material nonlinear, double nonlinear under different initial geometric defects are considered. The results show that the instability mode of arch trusses are all asymmetric instability of plane, and that the buckling load of considering double nonlinear is 13.84% that of considering geometry nonlinear, and that the coupling effect of geometry nonlinear and material nonlinear has accelerated reducing the stiffness of structure and bearing stable capacity ,and that the ratio for the buckling load of the four arch trusses with L/500, L/400, L/300 and L/200 initial geometric defects is 1.0: 0.927: 0.904: 0.87: 0.804, and that load-displacement process curves of feature node are the same change for the structures under different initial geometric defects.

Study on Elasto-Plastic Stability Bearing Capacities for K6 Single-Layer Reticulated Shells under Fire Conditions

The elastic modulus of steel will decrease in case of high temperature which makes the reticulated shells easier to have the global instability phenomenon. In order to obtain the elasto-plastic stability bearing capacities for K6 single-layer reticulated shells [1], nonlinear finite analysis compete process was conducted by ANAYS software under on the two typical cases which include global non-uniform temperature distribution and localized high temperature. Based on the calculation formula for single-layer reticulated shells at ambient temperature, the calculation formula for elasto-plastic stability bearing capacity for K6 single-layer reticulated shells was obtained.

Elasto-plastic stability of single-layer reticulated domes with initial curvature of members

Initial curvature of members is an inevitable geometrical imperfection for reticulated domes. To investigate the stability of single-layer domes with initial curvature of members, the multi-beam method was presented to simulate the initial curvature of members, and two modeling methods were adopted to introduce the initial curvature of members for reticulated domes by means of ANSYS. First, the random imperfection mode method was introduced according to the randomness of initial curvature of members. The example of a Kiewitt-8 dome was used to explain the method and investigate the influence of angle and amplitude random variables on the stability of reticulated domes. Second, the modified consistent imperfection mode method was obtained, which was an efficient method to evaluate the lowest buckling load of the structure with initial curvature of members. Based on this method, the Kiewitt-6 and Kiewitt-8 single-layer reticulated domes were taken as examples to analyze the stability of structures with initial curvature of members, and the influences of initial curvature of members on the ideal structure and the structure with nodes deviation were obtained quantitatively. The results show that, for the ideal structure and the structure with nodes deviation, initial curvature of members can decrease the buckling load of the structure obviously. Initial curvature of members can change the buckling mode and plasticity development of the structure. The influence of initial curvature of members on the elasto-plastic stability of single-layer reticulated domes cannot be neglected.

Elasto-Plastic Stability Analysis of a Twin Continuous Rigid Frame Bridge with 195m High Single Pier

Aiming at 195m high single pier of Hezhang Bridge, elasto-plastic stability analysis on static wind loads and temperature gradients at the longest cantilevered stage for single pier has been performed by ANSYS software. To overcome the problem on buckling of main girder ahead of piers, a loading way with concentrated force instead of uniform load was presented. A general expression of beam element-based temperature distribution along pier was given. Stability analysis under three different actions of wind load at the longest cantilevered stage was conducted according to Chinese Wind-resistent Design Specification for Highway Bridges. The results show that whatever static wind load or thermal gradient effect is, the inelastic stability factors against buckling are all over 3.0 and satisfy the engineering requirement.

Elasto-plastic stability of single-layer reticulated shells

Investigation of elasto-plastic stability of reticulated shells has gradually become more and more attractive to researchers. However, the analysis of the elasto-plastic stability is much more complicated than the elastic analysis, because of the involvement of both the geometrical nonlinearity and the material nonlinearity and the interactions of the two. Taking into consideration of material nonlinearity, the elasto-plastic stability behaviour of reticulated shells will be significantly different, which can only be revealed by large amount of geometrically and material nonlinear analysis of the structures. The elasto-plastic stability of seven types of commonly used single-layer reticulated shells (Kiewitt-8, Kiewitt-6, Geodesic, Schwedler Bidirectional, Schwedler Monoclonal, Sunflower, and Radial Rib) was investigated systematically with ANSYS, in which more than 2000 cases of geometrically and material nonlinear analysis were conducted with different initial geometrical imperfections, geometrical, structural and load parameters. Based on the analytical results and via comparison between elastic and elasto-plastic buckling loads, the plasticity influence coefficients were summarized for each type of the reticulated domes. These coefficients can be used to predict accurately the elasto-plastic buckling load in design practice of the reticulated domes, which is an easy way for designers to evaluate stability of the reticulated shells.

Non-linear dynamic behaviour of multi-folding microstructure systems based on origami skill

This paper presents the theoretical basis for both static and dynamic numerical approaches to the elastic stability and elasto-plastic stability of a folding multi-layered truss. Both analyses are based on bifurcation theory and include geometrical non-linearity. The dynamic analysis includes an allowance for contact between nodes. Comparisons are made between elastic behaviour and elasto-plastic behaviour obtained from both numerical dynamic methods in which bifurcations are demonstrated as a theoretically elastic analysis. Our analysis reveals that several folding behaviours in the pantographic truss are identified during the elastic and elasto-plastic instabilities, where the folding behaviour of the truss is shown to be a function of the initial geometry and velocity of the dynamic loading. The authors suggest that understanding this behaviour will be very useful for developing light-weight structures subject to dynamic loading based on static bifurcation analysis and dynamic analysis.

Elastoplastic analysis of thin-walled structures in reservoir area

In the structural design of the high pier, in order to analyze the strength and structure stability, the pier was often considered a thin-walled structure. Elastoplastic incremental theory was used to establish the model of elastoplastic stability of high pier. By considering the combined action of pile, soil and pier together, the destabilization bearing capacity was calculated by using 3-D finite element method (3-D FEM) for piers with different pile and section height. Meanwhile, the equivalent stress in different sections of pier was computed and the processor of destabilization was discussed. When the pier is lower, the bearing capacity under mutual effect of pile, soil and pier is less than the situation when mutual effect is not considered; when the pier is higher, their differences are not conspicuous. Along with the increase of the cross-sectional height, the direction of destabilization bearing capacity is varied and the ultimate capacity is buildup. The results of a stability analysis example are almost identical with the practice.

Elastoplastic stability analysis of mine haulage drift in the vicinity of mined stopes

This paper is focused on the interaction between the haulage drift and nearby mining activity related to sublevel stoping method with delayed backfill, one of the most popular mining methods in Canadian underground metal mines. The stability of the haulage drift is examined through a detailed parametric study of a nonlinear, elastoplastic, two-dimensional finite element model representing typical mining layout most commonly adopted in Canadian underground metal mines. The model parametric study examines the influence of critical factors such as the stope mining sequence, mining depth and the distance between the stope and the haulage drift. Stability indicators are defined in terms of displacement, stress and the extent of yield zones, which serve as a basis for assessing the effect of different parameters on the stability of the haulage drift. The model parametric study demonstrates that stope mining causes a footwall lateral shift of the entire drift. The severity of such shift is increased with shorter distance between the stope and haulage drift. Of all mining excavations examined, same-level mining appears to be the most critical. It is also found that more stress relaxation zones and yield zones develop around the haulage drift as the mining depth increases and as distance between haulage drift and the stope decreases.