Mahmoud S. M. Shaqfa

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A virtual microstructure generator for 3D stone masonry walls

Katrin Beyer, Mahmoud S. M. Shaqfa

Detailed micromodel simulations of stone masonry walls require as input a 3D mesh that represents a realistic arrangement of stones in the masonry wall. In this paper, we constructed the first 3D masonry microstructures to derive 2D and 3D finite or discrete element meshes for a large range of stone and brick masonry typologies. The generation process was treated as a constraint many-objectives packing optimisation problem, which was designed to mimic the building process of a mason. The generated walls were compared qualitatively and quantitatively with real stone masonry samples of regular and irregular typologies. The Python3.7 codes of the microstructure generator and the generated meshes shown in this paper are all made available under GNU LGPLv3 terms and conditions. The techniques in this paper for generating 3D meshes of stone masonry walls will serve as input for simulations of individual walls, multiscale analyses of entire structures as well as for homogenisation techniques.

ELSEVIER2022

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As historical stone masonry structures are vulnerable and prone to damage in earthquakes, investigating their structural integrity is important to reduce injuries and casualties while preserving their historical value. Stone masonry is a composite material that is built with stones and binding mortar. Although experimental campaigns are crucial in understanding the structural behaviour of these walls, the wide spectrum of existing stone masonry typologies and the randomness in geometry and material properties render extensive testing campaigns nearly impossible to account for all the uncertainties and variables. Numerical simulations that explicitly represent the microstructure of the wall (i.e., the geometry and arrangement of the stones) can complement experimental studies. However, methods for generating 3D microstructures were lacking.The focus of this dissertation is to study the geometry of the 3D microstructure of stone masonry walls at multiple scales, which opens unprecedented opportunities for studying the micromechanical behaviour of these walls numerically. The first contribution of this thesis was crafting the first 3D virtual microstructure generator that can cover the main typologies of stone masonry that are frequently found in historical buildings. The herein-created microstructure generator borrowed the conventional packing problem analogy to pack the generated stones inside the boundary of the walls following building and physical placement rules to obtain realistic microstructures. The size spectrum, distribution, interlocking and topology of the generated stones were thoroughly investigated. To quickly and efficiently solve the posed packing problem of each stone, we proposed a general-purpose heuristic algorithm that benefits from Pareto's principle which is commonly known as the

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rule. This heuristic was called the Pareto sequential sampling (PSS) algorithm as it depends on sampling most of the solutions, using any design of experiment (DoE) method, from a domain that is known to be a prominent pool of solutions.The second contribution was related to studying the topology and roughness of stones and surfaces. The traditional spherical harmonics expansion was used to study the morphology of closed surfaces of the nonconvex stones to estimate their fractal dimension and uniformly remesh the triangulated surfaces to be used in numerical simulations. As the roughness of natural stones changes on a single stone, we similarly studied the morphology of locally sampled rough patches. We developed the spherical cap harmonics and disk harmonics spectral approaches to provide us with information on the roughness and fractal dimension of any isotropic self-affine rough surface. To speed up the numerical integration of these spectral expansions, we proposed new algorithms based on the well-known Kaczmarz orthogonal projection in a non-memory-intensive manner and using reasonable computational times. The developed algorithms were hinged on the conjugate symmetry of the harmonic bases and the sparsity of the real signals to lower the dimensionality of the problem and accelerate the rate of convergence. These spectral methods are considered general-purpose and have multiple applications in various fields such as medical imaging and computer graphics. With this dissertation, we put forward geometrical and topological concepts that make detailed micromechanical simulations of stone masonry walls practical.

EPFL2022

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Pareto-like sequential sampling heuristic for global optimisation

Katrin Beyer, Mahmoud S. M. Shaqfa

In this paper, we propose a simple global optimisation algorithm inspired by Pareto’s principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the dynamic tightening of the prominent domains while the greediness of the algorithm increases over time (iterations). Unlike traditional metaheuristics, the proposed method has no direct mutation- or crossover-like operations. It depends solely on the sequential random sampling that can be used in diversification and intensification processes while keeping the information-flow between generations and the structural bias at a minimum. By using a simple topology, the algorithm avoids premature convergence by sampling new solutions every generation. A simple theoretical derivation revealed that the exploration of this approach is unbiased and the rate of the diversification is constant during the runtime. The trade-off balance between the diversification and the intensification is explained theoretically and experimentally. This proposed approach has been benchmarked against standard optimisation problems as well as a selected set of simple and complex engineering applications. We used 26 standard benchmarks with different properties that cover most of the optimisation problems’ nature, three traditional engineering problems, and one real complex engineering problem from the state-of-the-art literature. The algorithm performs well in finding global minima for nonconvex and multimodal functions, especially with high dimensional problems and it was found very competitive in comparison with the recent algorithmic proposals. Moreover, the algorithm outperforms and scales better than recent algorithms when it is benchmarked under a limited number of iterations for the composite CEC2017 problems. The design of this algorithm is kept simple so it can be easily coupled or hybridised with other search paradigms. The code of the algorithm is provided in C++14, Python3.7, and Octave (Matlab).

2021

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EPFL2022