A Review of Elasto-Plastic Shakedown Analysis with Limited Plastic Deformations and Displacements

In classical plasticity the shakedown analysis is among the most important basic problems. The principles of shakedown analysis are counterparts to those of limit analysis in the sense that they provide static and kinematic approaches to the question of whether or not shakedown will occur for a body under multiple variable loading conditions. The principles of limit analysis provide static and kinematic approaches to the question of whether or not the plastic limit state will be reached by a body under proportional loading. The principles of shakedown analysis are, however, considerably more difficult to apply than those of limit analysis. In spite of these difficulties, shakedown analysis is a vital and developing topic in plasticity and a great number of applications have been made. At the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the shakedown analysis provide no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore for their determination bounding theorems and approximate methods have been proposed

Reliability Based Analysis and Optimum Design of Laterally Loaded Piles

In this study reliability based limit analysis is used to determine the ultimate capacity of laterally loaded piles.  The aim of this study is to evaluate the lateral load capacity of free-head and fixed-head long pile when plastic limit analysis is considered. In addition to the plastic limit analysis to control the plastic behaviour of the structure, uncertain bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect for the load parameter. The solution to reliability-based problems is based on a direct integration technique and the uncertainties are assumed to follow Gaussian distribution. The optimization procedure is governed by the reliability index calculation

An Investigation of the Recent Developments in Reliability-based Structural Topology Optimization

Optimizing a structure's topology involves finding the best possible distribution of material and connections within a given design space. It has a significant effect on its performance, which is why there has been a meteoric rise in the number of articles published on the topic over the last two decades. This work offers an investigation of reliability-based topology optimization of structures, in light of the recent development of several topology optimization techniques for both linear and nonlinear systems. Therefore, the emphasis of this study is on the latest advancements, enhancements, and applications of reliability-based topology optimization. This paper's primary objective is to provide an overview of the latest advancements in the reliability-based topology optimization of structures, with a particular emphasis on the recent improvement of integrating reliability-based design into the bi-directional evolutionary structural optimization (BESO) method, which accounts for the topological optimization of geometric and material nonlinearity as well as thermoelastic problems

DEM Modeling of Crushable Grain Material under Different Loading Conditions

This paper deals with the effect of contact conditions on the crushing mechanisms and the strength of granular materials. The computation of crushable grain material under different loading conditions is performed using 3D model of discrete element method (DEM). The crushable macro-grain is generated from a large number of identical spherical micro-grains which are connected according to the bonded particle model. First, the parameters of the proposed DEM model are calibrated to match the force-displacement curve obtained from Brazilian Tests performed on cylinders made of artificially crushable material. The damage profile right at the point when the force-displacement curve reaches its maximum is seen to replicate the same crack patterns observed in Brazilian test experiments. Then, parametric investigations are performed by varying the coordination number, the contact location distribution, and the contact area. The results show that these parameters play a significant role in determining the critical contact force and fracture mechanism of crushable particles compared to a traditional macro-grain crushing test. Increasing distribution and coordination number of the macro-grain increases particle strength when large area contact is permitted. However, for linear contact area, the effect of increasing coordination number on particle strength is marginal

Optimal Plastic Analysis and Design of Pile Foundations Under Reliable Conditions

In this research, in order to evaluate the plastic limit load and also plastic design parameters of the long pile foundations subjected to horizontal loads, shakedown method is applied. In carrying out shakedown analysis and design methods, large plastic deformations and residual displacements could develop in the pile foundation which might lead to the failure of the structure. For this reason, complementary strain energy of residual forces proposed as a limit condition to control the plastic deformation of the pile structure. Furthermore, considering the uncertainties (strength, manufacturing, geometry) the limit conditions on the complementary strain energy of residual forces are assumed randomly and the reliability condition was formed by the use of the strict reliability index. The influence of the limit conditions on the plastic limit load and design parameters of the long pile in cohesionless soil subjected to lateral load were investigated and limit curves for shakedown load factors are presented. The numerical results show that the probabilistic given limit conditions on the complementary strain energy of residual forces have significant influence on the load bearing limit and the design parameters of pile foundations. The formulations of the reliability based problems lead to mathematical programming which were carried out by the use of non-linear algorithm

Influence of the Loading Condition on Single Grain Crushing in DEM Simulation

Grain crushing is of essential importance for understanding the mechanical behavior of granular materials such as sand, gravel or broken rock under higher pressures. In order to investigate the breakage mechanism of a single grain under different loading conditions, numerical simulations are carried out using DEM. Two different types of boundary conditions are considered to apply displacement-controlled load: loading using platens and loading by uncrushable macro-grains. A 2D crushable macro-grain is built up from a large number of micro-grains which are connected with respect to breakable parallel-bond properties. The response of the crushable macro-grain for different coordination numbers and location of the contact points is discussed. The numerical results show that the type of loading condition can influence the loading capacity and fragmentation patterns of the crushable macro-grain

Laboratory Investigation on the Effect of Microsilica Additive on the Mechanical Behavior of Deep Soil Mixing Columns in Saline Dry Sand

Since loose and salty subgrades consider as problematic barriers while constructing new transportation infrastructures such as railway tracks and roads are required, the current study aims to find a solution to stabilize these kinds of subgrades using the deep soil mixing (DSM) technique and micro silica additive. In the present study a series of experimental DSM columns were executed in a salty sand-filled chamber utilizing a laboratory scale DSM apparatuses. In the first step, by adding three salt percentages of 5, 10 and 20 into the original sand, four different sandy subgrades with a relative density of 70% were prepared. Considering three percentages of 10, 15 and 20 for micro silica additive, the water-to-cement ratio of 1, salt percentages of 0, 5, 10 and 20 totally 150 sand-cement columns were constructed in the lab environment. In continuation, unconfined compression strength (UCS) and elasticity modulus of all capped DSM columns have been determined and interpreted using scanning electron microscope (SEM) images at three ages of 7,14 and 28 days. The results indicated that increasing the salinity of subgrade soil from 0 to 20% resulted in a falling UCS and Young module by 28 and 21% for 28-days specimens. Furthermore, as a solution, adding micro silica in cement-water grout up to 15% resulted in enhancing mechanical characteristics of the DSM columns. So that adding 15% microsilica caused a 21 and 42% increase in UCS and elasticity modulus of 28-days samples respectively, executed in subgrade with 20% salt

Reliability based design of frames with limited residual strain energy capacity

The aim of this paper is to create new type of plastic limit design procedures where the influence of the limited load carrying capacity of the beam-to-column connections of elasto-plastic steel (or composite) frames under multi-parameter static loading and probabilistically given conditions are taken into consideration. In addition to the plastic limit design to control the plastic behaviour of the structure, bound on the complementary strain energy of the residual forces is also applied. If the design uncertainties (manufacturing, strength, geometrical) are taken into consideration at the computation of the complementary strain energy of the residual forces the reliability based extended plastic limit design problems can be formed. Two numerical procedures are elaborated. The formulations of the problems yield to nonlinear mathematical programming which are solved by the use of sequential quadratic algorithm

Optimizing Topology of Structures Considering Fatigue-Resistance

The pursuit of reliable design has become increasingly crucial in various engineering disciplines, aiming to minimize environmental impact and enhance resource efficiency. In this context, this study explores the integration of topology optimization techniques with fatigue analysis to develop reliable designs for structural components. Fatigue failure is a critical concern in engineering applications, as it significantly affects the lifespan and reliability of structures. The proposed methodology combines mathematical optimization algorithms, computational modeling, and fatigue analysis techniques. The primary objective of this study is to minimize structural weight by determining the optimal material arrangement within the design domain while also considering fatigue as a constraint within the optimization problem. The bi-directional evolutionary structural optimization (BESO) method is developed to meet the goal of this research. Furthermore, topology optimization of L-shape and U-plate problems are considered as numerical examples to demonstrate the effectiveness of the suggested method. By considering fatigue behavior in topology optimization, engineers can develop lightweight and durable structures that effectively utilize materials while minimizing resource utilization. The integration of these two fields opens up new avenues for reliable design, promoting resource efficiency and contributing to the overall reliability of engineering practices