Determination of strut-and-tie models using evolutionary structural optimization

This paper examines the evolutionary structural optimisation (ESO) method and its shortcomings. By proposing a problem statement for ESO followed by an accurate sensitivity analysis a framework is presented in which ESO is mathematically justifiable. It is shown that when using a sufficiently accurate sensitivity analysis, ESO method is not prone to the problem proposed by Zhou and Rozvany (Struct Multidiscip Optim 21(1):80---83, 2001). A complementary discussion on previous communications about ESO and strategies to overcome the Zhou-Rozvany problem is also presented. Finally it is shown that even the proposed rigorous ESO approach can result in highly inefficient local optima. It is discussed that the reason behind this shortcoming is ESO's inherent unidirectional approach. It is thus concluded that the ESO method should only be used on a very limited class of optimisation problems where the problem's constraints demand a unidirectional approach to final solutions. It is also discussed that the Bidirectional ESO (BESO) method is not prone to this shortcoming and it is suggested that the two methods be considered as completely separate optimisation techniques.

Topology optimization of the inner reinforcement for a vehicle’s hood has been performed by evolutionary structural optimization (ESO) method. The purpose of this study is to obtain optimal topology of the inner reinforcement for a vehicle’s hood considering static stiffness and natural frequency simultaneously. To do this, the multiobjective design optimization technique was implemented. From several combinations of weighting factors, a Pareto-optimal solution was obtained. Optimal topologies were obtained by the ESO method, i.e., by eliminating the elements having the lowest efficiency from the structural domain. As the weighting factor of the elastic strain efficiency goes from 1 to zero, it is found that the optimal topologies transmits from the optimal topology of static stiffness problem to that of natural frequency problem. Therefore, it was concluded that ESO method is effectively applied to topology optimization of the inner reinforcement of a vehicle’s hood.

The Evolutionary Structural Optimization (ESO) has been applied to find the optimal structural topology for design and construction purposes. However, its efficiency is low due to the imperfect deletion criteria. This paper presents an improved elimination criterion and the Windowed Evolutionary Structural Optimization (WESO) method. The former considers the structural average strain energy as the elimination criteria in the optimization, with the elimination rate set as a self-adaption state by an adjustable window. Thus, the problems of low optimization efficiency and distorted optimization results in the traditional ESO can be solved to a certain extent. The WESO method can then be extended and applied with a complex finite element model. It is found that the method has better optimal ability in handling discrete elements in vast structures. Compared with the other method, the WESO method has high computational efficiency and offers more stable and reliable topology than the Michell theoretical solution. Lastly, upon developing the optimal topology for a double-deck structure, it is shown that the WESO method has a great potential in civil engineering applications.

Owing to advancement in advanced manufacturing technology, the reinforcement design of concrete structures has become an important topic in structural engineering. Based on bi-directional evolutionary structural optimization (BESO), a new approach is developed in this study to optimize the reinforcement layout in steel-reinforced concrete (SRC) structures. This approach combines a minimum compliance objective function with a hybrid truss-continuum model. Furthermore, a modified bi-directional evolutionary structural optimization (M-BESO) method is proposed to control the level of tensile stress in concrete. To fully utilize the tensile strength of steel and the compressive strength of concrete, the optimization sensitivity of steel in a concrete–steel composite is integrated with the average normal stress of a neighboring concrete. To demonstrate the effectiveness of the proposed procedures, reinforcement layout optimizations of a simply supported beam, a corbel, and a wall with a window are conducted. Clear steel trajectories of SRC structures can be obtained using both methods. The area of critical tensile stress in concrete yielded by the M-BESO is more than 40% lower than that yielded by the uniform design and BESO. Hence, the M-BESO facilitates a fully digital workflow that can be extremely effective for improving the design of steel reinforcements in concrete structures.

The principal purpose of this paper is to present an AC experimental data (alternative current) impedance testing method. The least squares technique is used to perform mathematical analysis for the numerical value based on the experimental data and desired curve fitting equation to find the approximate function that is the most probable for expressing the experimental data. Moreover, the Kramers‐Kronig transforms, Bode and Nyquist plots are used to present the electric equivalent circuits such as the Randles, diffusion, Wenger and John models which are for predicting the corrosion state of RC (reinforced concrete) structures. According to the AC impedance testing data, the parameter values of each element of the four electric equivalent circuits can be found. This study denotes that the resistance value can be applied for corrosion prevention in RC structures while the capacitance value can be employed to judge the corrosion rate for RC structures. The analyzed results were used to predict the state of existing RC structures.

Since efficient material usage in a structure is an essential intention in engineering design, objective of a structural optimization algorithm should be obtaining the lightest and stiffest structure while considering specific design constraints. Evolutionary structural optimization (ESO) method has been introduced by Xie and Steven in 1993 to overcome structural optimization problems by improving and optimizing the design of structures. Although the algorithm depends on a plain inspiration, performance level of the ESO algorithm has increased owing to the contributions of wide-ranging studies in the subsequent years. This heuristic method has appeared on a simple—sometimes defined as intuitive—idea that is eliminating (or removing) the inefficient elements from the initial design region and attaining a fully stressed structure with an updated topology. Such a process is performed iteratively until an optimum layout is achieved, or until a specified volume is acquired; and the decision of process termination is executed over the feasibility of the designs achieved. This optimization algorithm is based on finite element method and has showed its superiorities by subsequent studies in various disciplines. Within this chapter, a brief on the basis and the main improvement steps of evolutionary structural optimization is presented. Different approaches on objectives, constraints, processing and terminating will be summarized. Thereafter, efficiency and capability of the method will be demonstrated over some examples.

This study presents an investigation on the design of long reinforced concrete (RC) structures subjected to uniform temperature load by considering three RC frame building models with different lengths of 45 m, 135 m, and 270 m using Etabs. The uniform temperature load is considered being the change from the annual average highest to lowest air temperature at the construction site in the case of unavailable temperature data of concrete. The analysis results indicate that the uniform temperature load mainly influences on the internal forces of RC members at storey 1 and slightly effects on the internal forces of RC members at storey 2. For short-length RC structures, the effect of temperature load can be ignored in the design of RC elements, whereas it must be taken into account in design of slab, beams and some column positions at storey 1 of medium-length and long RC structures without expansion joints. For the present RC frame building models, the required slab reinforcement in long direction increases about 33.4% for medium-length RC structures (135 m) and about 48.2% for long RC structures (270 m) without expansion joints. The required reinforcement for positive moment at mid-span increases from 33.7 to 39.4%, whereas the total required reinforcement for negative moment at the supports of beams increases from 19.4 to 34.9% in long direction of 270 m long RC structures without expansion joints due to uniform temperature load. Column design of long RC structures without expansion joints under uniform temperature load must be concerned, especially for columns in the corners.

The evolutionary structural optimization (ESO) method developed by Xie and Steven (Comput Struct 49(5):885–896, 162), an important branch of topology optimization, has undergone tremendous development over the past decades. Among all its variants, the convergent and mesh-independent bi-directional evolutionary structural optimization (BESO) method developed by Huang and Xie (Finite Elem Anal Des 43(14):1039–1049, 48) allowing both material removal and addition, has become a widely adopted design methodology for both academic research and engineering applications because of its efficiency and robustness. This paper intends to present a comprehensive review on the development of ESO-type methods, in particular the latest convergent and mesh-independent BESO method is highlighted. Recent applications of the BESO method to the design of advanced structures and materials are summarized. Compact Malab codes using the BESO method for benchmark structural and material microstructural designs are also provided.

The “hard-kill” optimization methods such as evolutionary structural optimization (ESO) and bidirectional evolutionary structural optimization (BESO) may result in a nonoptimal design (Zhou and Rozvany in Struct Multidisc Optim 21:80–83, 2001) when these methods are implemented and used inadequately. This note further examines this important problem and shows that failure of ESO may occur when a prescribed boundary support is broken for a statically indeterminate structure. When a boundary support is broken, the structural system could be completely changed from the one originally defined in the initial design and even BESO would not be able to rectify the nonoptimal design. To avoid this problem, it is imperative that the prescribed boundary conditions for the structure be checked and maintained at each iteration during the optimization process. Several simple procedures for solving this problem are suggested. The benchmark problem proposed by Zhou and Rozvany (Struct Multidisc Optim 21:80–83, 2001) is revisited, and it is shown that the highly nonoptimal design can be easily avoided.

The purpose of this study was to develop a new element removal method for ESO (Evolutionary Structural Optimization), which is one of the topology optimization methods, ESO starts with the maximum allowable design space and the optimal topology emerges by a process of removal of lowly stressed elements. The element removal ratio of ESO is fixed throughout topology optimization at 1 or 2%. BESO (bidirectional ESO) starts with either the least number of elements connecting the loads to the supports, or an initial design domain that fits within the maximum allowable domain, and the optimal topology evolves by adding or subtracting elements. But the convergence rate of BESO is also very slow. In this paper, a new element removal method for ESO was developed for improvement of the convergence rate. Then it was applied to the same problems as those in papers published previously. From the results, it was verified that the convergence rate was significantly improved compared with ESO as well as BESO.

On various aspects of evolutionary structural optimization for problems with stiffness constraints

The demand for the construction of multi-story buildings is increasing rapidly due to growing competition and the need for more economical and spacious buildings.Theoretical calculations for such structures are critical and there is a growing demand for fast software to speed up the process.This dissertation uses computer program such as ETABS to design and analyze a multi-story building in two forms i.e.R.C.C and Composite Structure.The Indian design code is used for the design and the structure analyzed is an R.C.C and Composite Structure with 10 story.The seismic performance of structures is a critical factor in designing and constructing buildings in seismicprone regions.This dissertation presents a comparative study of the seismic resistance of Composite and Reinforced Concrete (RCC) structures under different medium soil conditions and seismic zones (II-Nagpur, III-Pune, IV-Delhi, V-Srinagar) using the ETABS software.The project evaluates the performance of composite and RCC structures in terms of lateral deflection, story drift, and base shear values and compares their response using the Response Spectrum Method and Time History Method.The study investigates the effects of different seismic zones (II-Nagpur, III-Pune, IV-Delhi, and V-Srinagar) and soil conditions (Rock or Hard soil, Medium soil, Soft soil) on the seismic resistance of these structures.The design of the structure follows the Indian design code, which includes the following codes: IS 456:2000, IS Code 800, IS Code 1893:1984, and IS Code 11384:1985 and so on.Composite structures are found to be the best mode of construction for high-rise building while comparing with the conventional R.C.C structures as they serve well for various parameters like lateral deflection, story drift and base shear values.The findings of this study can assist in selecting the most efficient and reliable type of structure for seismic resistance in different seismic zones and medium soil conditions.

A strength-based multiple cutout optimization in composite plates using fixed grid finite element method

Strain energy evolution characteristics and mechanisms of hard rocks under true triaxial compression

Automated clash resolution for reinforcement steel design in concrete frames via Q-learning and Building Information Modeling