Structural optimization in steel structures, algorithms and applications

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Optimal preliminary design of variable section beams criterion

AbstractThe present paper discusses about optimal shape solution for a non-prismatic planar beam. The proposed model is based on the standard Timoshenko kinematics hypothesis (i.e., planar cross-section remains planar in consequence of a deformation, but it is able to rotate with respect to the beam center-line). The analytical solution for this type of beam is thus used to obtain deformations and stresses of the beam, under different constraints, when load is assumed as the sum of a generic external variable vertical one and the self-weight. The solution is obtained by numerical integration of the beam equation and constraints are posed both on deflection and maximum stress under the hypothesis of an ideal material. The section variability is, thus, described assuming a rectangular cross section with constant base and variable height which can be described in general with a trigonometric series. Other types of empty functions could also be analyzed in order to find the best strategy to get the optimal solution. Optimization is thus performed by minimizing the beam volume considering the effects of non-prismatic geometry on the beam behavior. Finally, several analytical and numerical solutions are compared with results existing in literature, evaluating the solutions' sensibility to some key parameters like beam span, material density, maximum allowable stress and load distribution. In conclusion, the study finds a critical threshold in terms of emptying function beyond which it is not possible to neglect the arch effect and the curvature of the actual axis for every different case study described in this work. In order to achieve this goal, the relevance of beam span, emptying function level and maximum allowable stress are investigated

Experimental Investigation of the Static and Dynamic behaviors of 3D-Printed Shell Structures

Over the last years, several optimization strategies were conducted to find the optimal shape minimazing internal stress or total weight (volume) of shell structures. In recent times, this structure typology gained a great importance among researchers and the scientific community for the renowed interest in the form-findind optimization of column-free space solution for large span roofing constructions. In the present paper, a form-finding of a shallow grid shells was introduced basing on the multy-body rope approach (MRA) for the definitions of vault shapes and different hole percentage. In order to obtain an experimental validation, a physical model was reproduced at the laboratory scale performing ad hoc measurements to compare the observed respect to the simulated behaviour. A 3D printing procedure based on the Fuse Deposition Modeling (FDM) technique in polylactide (PLA) material was used to realise form-works of the cement based blocks of the scaled prototype. Several static and dynamic load configurations are investigated, collecting into a sensitivity analysis the parameters which mainly affect the structural behaviour. To simulate earthquake ground motion an assigned frequency range as dynamic input to the structure was provided by a shaking table. Finally, some preliminary considerations of the dynamic response of the model were provided testing the robustness of the form-finding approach when horizontal load are taken into account

Estimation of Distribution Algorithm for Constrained Optimization in Structural Design

Nowadays, the need to deal with limited resources together with the newly discovered awareness of the human over-exploitation of the environment, has made the optimization a cutting edge topic both in scientific research and in the different professional fields. In this paper, a particular evolutionary optimization algorithm is presented: The Estimation of Distribution Algorithm (EDA). This type of algorithm has been developed to be used in search-based constrained optimization problems which are difficult and time-consuming to be solved by other general algorithms. Being an evolutionary algorithm, the main idea is to generate a population of solutions and evaluate the objective function of each one of them. Then, using the information obtained from the previous generations, the algorithm step-by-step will generate new populations that will tend to the best value of the objective function. In EDA, the population of solutions defines a probability density function (PDF) and, by integration, a cumulative density function (CDF), which is used for the generation of the next generation. In structural design optimization problems, it is very common that the best solution is very close to the constraint function. The main advantage of applying the EDA for constrained optimization problems is that each generation of solutions is obtained starting from a PDF that is defined on the whole domain. This means that, for each generation, the solutions have a probability to be on the unfeasible domain space, maintaining the information about the objective function in the evolution process. In the present research, an original EDA and related self-made code are presented together with a specific application to structural optimization problems, in order to show the effectiveness of the obtained results and to make a comparison with other evolutionary optimization algorithms

Series solution of beams with variable cross-section

Abstract In structural engineering beams with non-constant cross-section or beams with variable cross-section represent a class of slender bodies, aim of practitioners' interest due to the possibility of optimizing their geometry with respect to specific needs. Despite the advantages that engineers can obtain from their applications, non-trivial difficulties occurring in the non-prismatic beam modeling often lead to inaccurate predictions that vanish the gain of the optimization process. As a consequence, an effective non-prismatic beam modeling still represents a branch of the structural engineering of interest for the community, especially for advanced design applications in large spans elements. A straight beam of length l with variable inertia J(z) is provided in figure, subject to a generic live load condition q(z). The vertical displacement y(z) can be obtained from the solution of the differential equation of the elastic line, i.e., taking into consideration the inertia variability and neglecting, as first approximation, any shear contribution. Even if this solution is an approximate one, it is able to deal with the problem in its basic formulation. In this paper a solution for the problem stated is formulated using a series expansion of solutions, in a general load and cross section variability condition. Solution is thus obtained for a generic rectangular cross section beam with a variable height. Analytical solution is presented and evaluated using numerical evaluation of some cases of practical interest

Advanced deep learning comparisons for non-invasive tunnel lining assessment from ground penetrating radar profiles

Innovative, automated, and non-invasive techniques have been developed by scientific community to indirectly assess structural conditions and support the decision-making process for a worthwhile maintenance schedule. Nowadays, machine learning tools are in the spotlight because of their outstanding capabilities to deal with data coming from even heterogeneous sources and their ability to extract information from the structural systems, providing highly effective, reliable, and efficient damage classification tools. In the current study, a supervised multi-level damage classification strategy has been developed regarding Ground Penetrating Radar (GPR) profiles for the assessment of tunnel lining conditions. In previous research, the authors firstly considered a convolutional neural network (CNN), adopting the quite popular ResNet-50, initialized through transfer learning. In the present work, further enhancements have been attempted by adopting two configurations of the newest state-of-art advanced neural architectures: the neural transformers. The foremost is the original Vision Transformer (ViT), whose core is an encoder entirely based on the innovative self-attention mechanism and does not rely on convolution at all. The second is an improvement of ViT which merges convolution and self-attention, the Compact Convolution Transformer (CCT). In conclusion, a critical discussion of the different pros and cons of adopting the above-mentioned different architectures is finally provided, highlighting the actual powerfulness of these technologies in the future civil engineering paradigm nevertheless

Enhanced Multi-Strategy Particle Swarm Optimization for Constrained Problems with an Evolutionary-Strategies-Based Unfeasible Local Search Operator

Nowadays, optimization problems are solved through meta-heuristic algorithms based on stochastic search approaches borrowed from mimicking natural phenomena. Notwithstanding their successful capability to handle complex problems, the No-Free Lunch Theorem by Wolpert and Macready (1997) states that there is no ideal algorithm to deal with any kind of problem. This issue arises because of the nature of these algorithms that are not properly mathematics-based, and the convergence is not ensured. In the present study, a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. State-of-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood). Furthermore, a new local search operator has been implemented to help localize the feasible region in challenging optimization problems. This operator is based on hybridization with another milestone meta-heuristic algorithm, the Evolutionary Strategy (ES). The self-adaptive variant has been adopted because of its advantage of not requiring any other arbitrary parameter to be tuned. This approach automatically determines the parameters’ values that govern the Evolutionary Strategy simultaneously during the optimization process. This enhanced multi-strategy PSO is eventually tested on some benchmark constrained numerical problems from the literature. The obtained results are compared in terms of the optimal solutions with two other PSO implementations, which rely on a classic penalty function approach as a constraint-handling method

Enhanced Multi-Strategy Particle Swarm Optimization for Constrained Problems with an Evolutionary-Strategies-Based Unfeasible Local Search Operator

Nowadays, optimization problems are solved through meta-heuristic algorithms based on stochastic search approaches borrowed from mimicking natural phenomena. Notwithstanding their successful capability to handle complex problems, the No-Free Lunch Theorem by Wolpert and Macready (1997) states that there is no ideal algorithm to deal with any kind of problem. This issue arises because of the nature of these algorithms that are not properly mathematics-based, and the convergence is not ensured. In the present study, a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. State-of-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood). Furthermore, a new local search operator has been implemented to help localize the feasible region in challenging optimization problems. This operator is based on hybridization with another milestone meta-heuristic algorithm, the Evolutionary Strategy (ES). The self-adaptive variant has been adopted because of its advantage of not requiring any other arbitrary parameter to be tuned. This approach automatically determines the parameters’ values that govern the Evolutionary Strategy simultaneously during the optimization process. This enhanced multi-strategy PSO is eventually tested on some benchmark constrained numerical problems from the literature. The obtained results are compared in terms of the optimal solutions with two other PSO implementations, which rely on a classic penalty function approach as a constraint-handling method

Nonpenalty Machine Learning Constraint Handling Using PSO-SVM for Structural Optimization

Firstly formulated to solve unconstrained optimization problems, the common way to solve constrained ones with the metaheuristic particle swarm optimization algorithm (PSO) is represented by adopting some penalty functions. In this paper, a new nonpenalty-based constraint handling approach for PSO is implemented, adopting a supervised classification machine learning method, the support vector machine (SVM). Because of its generality, constraint handling with SVM appears more adaptive both to nonlinear and discontinuous boundary. To preserve the feasibility of the population, a simple bisection algorithm is also implemented. To improve the search performances of the algorithm, a relaxation function of the constraints is also adopted. In the end part of this paper, two numerical literature benchmark examples and two structural examples are discussed. The first structural example refers to a homogeneous constant cross-section simply supported beam. The second one refers to the optimization of a plane simply supported Warren truss beam. The obtained results in terms of objective function demonstrate that this new approach represents a valid alternative to solve constrained optimization problems even in structural optimization field. Furthermore, as demonstrated by the Warren truss beam problem, this new algorithm provides an optimal structural design which represents also a good solution from the technical point of view with a trivial rounding-off that does not jeopardize significantly the optimization design process

Train-Track-Bridge Interaction Analytical Model with Non-proportional Damping: Sensitivity Analysis and Experimental Validation

Recent studies related to the dynamic response of railway bridges focused on gradually increasing the model complexity of the train-bridge interaction, however, did not always discuss any experimental validation. In the present work, the authors analyse the role of the ballast in the dynamic train-track-bridge interaction (TTBI). The analytical response of Euler-Bernoulli (EB) beams is coupled with a distributed springs layer modelling the ballast. The two equations are solved with trainloads as elementary moving load excitation, avoiding too complex models. This non-classically damped problem has been solved with a Runge-Kutta finite-difference method with temporal-spatial discretization. Furthermore, the authors experimentally validated the mathematical TTBI solution, comparing it with the displacement response of a case study. Specifically, at first, experimental modal bending stiffness parameters have been estimated to provide a representative equivalent EB beam model. Thereafter, the coupling effects of the ballast have been considered with a sensitivity analysis of the modelling parameters. Finally, the optimization to the actual experimental response of the model provided an estimate of the vertical ballast stiffness and its damping. The relevant difference in the damping of the experimental and mathematical model evidences the fundamental role of the ballast in adsorbing vibrations induced by the train passages