Teaching learning-based optimization for design of cantilever retaining walls

A methodology based on Teaching Learning-Based Optimization (TLBO) algorithm is proposed for optimum design of reinforced concrete retaining walls. The objective function is to minimize total material cost including concrete and steel per unit length of the retaining walls. The requirements of the American Concrete Institute (ACI 318-05-Building code requirements for structural concrete) are considered for reinforced concrete (RC) design. During the optimization process, totally twenty-nine design constraints composed from stability, flexural moment capacity, shear strength capacity and RC design requirements such as minimum and maximum reinforcement ratio, development length of reinforcement are checked. Comparing to other nature-inspired algorithm, TLBO is a simple algorithm without parameters entered by users and self-adjusting ranges without intervention of users. In numerical examples, a retaining wall taken from the documented researches is optimized and the several effects (backfill slope angle, internal friction angle of retaining soil and surcharge load) on the optimum results are also investigated in the study. As a conclusion, TLBO based methods are feasible

Optimization of Pile Groups Under Vertical Loads Using Grey Wolf Optimizer

Construction of foundations or embankments on a soft/loose soil deposit causes major problems in terms of geotechnical engineering. The vertical loads transferred from the foundation can cause failure and/or extreme settlements in the soft/loose soil. Additional geotechnical precautions must be taken in order to prevent such problems. Construction of piles under foundations is a widely used method. Piles are defined as point bearing piles or friction piles depending on the embedded length of the pile in the stiff layer or rock. Generally it is preferred to construct pile groups under the foundations to reduce the effects of differential settlements and eccentricity. The interaction of a pile with the others in a group is defined as "group efficiency" and this interaction causes reduction in the load-bearing capacities of the piles. It is necessary to calculate the bearing capacity of a single pile correctly and estimate the optimum number of piles in the group to make a safe and economical design. In this paper, it is aimed to investigate the robustness of Grey Wolf optimization algorithm for optimization problems of pile groups under vertical loads. In order to compare the validity of Grey Wolf Optimization algorithm, Particle Swarm Optimization algorithm and Improved Harmony Search algorithm are used. The proposed methods are intended to help engineers to make fast, safe and economical designs for pile groups. In this study, only the bearing capacities and optimization of bored pile groups are discussed

Optimum design of reinforced concrete cantilever retaining walls

The aim of engineering designs is to obtain results with minimum cost that will provide safety conditions. But the most economical design ensuring security conditions may not be found within the options, even the designer is experienced. Especially in the design of reinforced concrete (RC) structures that consist from two materials with very different mechanical properties and unit costs, it may be more difficult to achieve this purpose. In this study, a methodology based on teaching-learning-based optimization (TLBO) was proposed for optimum design of RC cantilever retaining wall under the static and dynamic loads. During the optimization process, 29 design constraints including retaining wall stabilities (overturning, sliding and soil stress), section capacities (flexure and shear) and RC design rules are checked. In the optimization problem, totally 17 design variables (5 of them related to cross-section dimension and 12 of them related to RC design) are used. In the sizing of retaining wall, the rules of the TS 7994 (Soil Retaining Structures; Properties and Guidelines for Design) are considered. In the RC design, the requirements of the relevant regulations; TS 500 (Requirements for Design and Construction of Reinforced Concrete Structures) and DBYBHY (Specification for Buildings to be Built in Seismic Zones) are considered. The results obtained by the proposed method were compared with the existing methods and the method seems as suitable for the optimum design of the cantilever type RC retaining walls

Grey Wolf Optimizer for Optimum Design of Reinforced Concrete Cantilever Retaining Walls

In this study, optimum design of cantilever reinforced concrete cantilever retaining walls is investigated under static load conditions. A methodology based on a recently developed metaheuristic algorithm called grey wolf optimizer was proposed. As the objective function, the total cost of the retaining wall including concrete, steel, labor, transportation etc. is considered. The eleven design variables such as heel and toe projections, stem thickness at the top and bottom of the wall, slab thickness, diameters and spacing of reinforced bars in critical sections are considered in the optimization process. During the optimization, totally twenty-nine design constraints including overturning stability, sliding stability, bearing capacity (maximum and minimum soil stresses), flexural moment and shear capacities of the section, minimum and maximum reinforcement ratio, development length of the bars, spacing limits of the bars (maximum and minimum spacing) are checked for the security of the wall. The requirements of the American Concrete Institute (ACI 318 14: Building code requirements for structural concrete) are considered in the reinforced concrete design

EFFECTS OF THE ASSUMPTION ABOUT RIGID FLOOR DIAPHRAGM ON THE SHEAR ALONG THE SHEAR WALLS

The purpose of this study is to establish the effects of rigid floor assumption on shear forces that occurs on shear walls of building type structural systems. Before the advent of computers only limited number of equations could be solved manually. Thus, simplification methods have been developed to reduce the total processes. In the structural analysis of buildings, rigid floor assumption is one of these methods. At the mass center of each rigid floor, there is a master node having three degrees of freedom to represent the two in-plane translations and one out of plane rotation. In this study, the linear elastic design analysis is carried out modeling floors as rigid diaphragm and flexible diaphragm. Results of the analysis are presented comparatively. According to these results, as a consequence of rigid floor assumption, it can be an issue to get designed such buildings those construction costs are higher but structural safety is lower in comparison with flexible floor model

Resource Constrained Project Scheduling by Harmony Search Algorithm

The construction industry is nonhomogeneous and also managing construction projects are more difficult in today's world. Construction projects are huge and contractors want to accomplish them within a short time in this fast changing era. Therefore, the time and resource have to be managed for a successful construction project management. Resource leveling is one of the primary tools used for managing resources. The target is leveling the resources within a minimum time period to complete the project successfully. Resource constrained project scheduling problems (RCPSP) are a Non-deterministic Polynomial-time hard (NP-hard) problem therefore heuristic methods can be used to solve it. This paper presents a harmony search method for solving the RCPSP. In order to compare the performance of the developed software three examples were chosen from the literature. Computational results indicate that the harmony search method is more effective, rapid and suitable for the RCPSP than existing solutions

Computation of Nonunique Solutions for Trusses Undergoing Large Deflections

Determination of nonunique configurations of structures is a problem which cannot be treated readily using classical methods of analysis. In the literature, these kinds of problems are tackled for some simple problems, like trusses with a small number of joints and members, and with specially designed approaches. The recent method of analysis called Total Potential Optimization using Metaheuristic Algorithms (TPO/MA), on the other hand, provides an efficient tool for dealing with these kinds of problems, practically without recourse to any special arrangement. In this analysis, using Harmony Search as the metaheuristic algorithm, large truss structures with linear elastic members are investigated under large deflections as to the existence of more than one solution. The results have shown that for the two examples investigated, a tower truss with 25 members and a dome truss with 24 members, nonunique configurations do exist at quite unexpected levels of loads, and that only one of them can be found with normal applications of the well-known Finite Element method

Analysis of trusses by total potential optimization method coupled with harmony search

Current methods of analysis of trusses depend on matrix formulations based on equilibrium equations which are in fact derived from energy principles, and compatibility conditions. Recently it has been shown that the minimum energy principle, by itself, in its pure and unmodified form, can well be exploited to analyze structures when coupled with an optimization algorithm, specifically with a meta-heuristic algorithm. The resulting technique that can be called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) has already been applied to analyses of linear and nonlinear plane trusses successfully as coupled with simulated annealing and local search algorithms. In this study the technique is applied to both 2-dimensional and 3-dimensional trusses emphasizing robustness, reliability and accuracy. The trials have shown that the technique is robust in two senses: all runs result in answers, and all answers are acceptable as to the reliability and accuracy within the prescribed limits. It has also been shown that Harmony Search presents itself as an appropriate algorithm for the purpose

Analysis of cable structures through energy minimization

In structural mechanics, traditional analyses methods usually employ matrix operations for obtaining displacement and internal forces of the structure under the external effects, such as distributed loads, earthquake or wind excitations, and temperature changing inter alia. These matrices are derived from the well-known principle of mechanics called minimum potential energy. According to this principle, a system can be in the equilibrium state only in case when the total potential energy of system is minimum. A close examination of the expression of the well-known equilibrium condition for linear problems, P=K Delta, where P is the load vector, K is the stiffness matrix and A is the displacement vector, it is seen that, basically this principle searches the displacement set (or deformed shape) for a system that minimizes the total potential energy of it. Instead of using mathematical operations used in the conventional methods, with a different formulation, meta-heuristic algorithms can also be used for solving this minimization problem by defining total potential energy as objective function and displacements as design variables. Based on this idea the technique called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is proposed. The method has been successfully applied for linear and non-linear analyses of trusses and truss-like structures, and the results have shown that the approach is much more successful than conventional methods, especially for analyses of nonlinear systems. In this study, the application of TPO/MA, with Harmony Search as the selected meta-heuristic algorithm, to cables net system is presented. The results have shown that the method is robust, powerful and accurate