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In this thesis, a new approach is developed for applications of shape optimization on the time harmonic wave propagation (Helmholtz equation) for acoustic problems. This approach is introduced for different dimensional problems: 2D, 3D axi-symmetric and fully 3D problems. The boundary element method (BEM) is coupled with the isogeometric analysis (IGA) forming the so-called (IGABEM) which speeds up meshing and gives higher accuracy in comparison with standard BEM. BEM is superior for handling unbounded domains by modeling only the inner boundaries and avoiding the truncation error, present in the finite element method (FEM) since BEM solutions satisfy the Sommerfeld radiation condition automatically. Moreover, BEM reduces the space dimension by one from a volumetric three-dimensional problem to a surface two-dimensional problem, or from a surface two-dimensional problem to a perimeter one-dimensional problem. Non-uniform rational B-splines basis functions (NURBS) are used in an isogeometric setting to describe both the CAD geometries and the physical fields.
IGABEM is coupled with one of the gradient-free optimization methods, the Particle Swarm Optimization (PSO) for structural shape optimization problems. PSO is a straightforward method since it does not require any sensitivity analysis but it has some trade-offs with regard to the computational cost. Coupling IGA with optimization problems enables the NURBS basis functions to represent the three models: shape design, analysis and optimization models, by a definition of a set of control points to be the control variables and the optimization parameters as well which enables an easy transition between the three models.
Acoustic shape optimization for various frequencies in different mediums is performed with PSO and the results are compared with the benchmark solutions from the literature for different dimensional problems proving the efficiency of the proposed approach with the following remarks:
- In 2D problems, two BEM methods are used: the conventional isogeometric boundary element method (IGABEM) and the eXtended IGABEM (XIBEM) enriched with the partition-of-unity expansion using a set of plane waves, where the results are generally in good agreement with the linterature with some computation advantage to XIBEM which allows coarser meshes.
-In 3D axi-symmetric problems, the three-dimensional problem is simplified in BEM from a surface integral to a combination of two 1D integrals. The first is the line integral similar to a two-dimensional BEM problem. The second integral is performed over the angle of revolution. The discretization is applied only to the former integration. This leads to significant computational savings and, consequently, better treatment for higher frequencies over the full three-dimensional models.
- In fully 3D problems, a detailed comparison between two BEM methods: the conventional boundary integral equation (CBIE) and Burton-Miller (BM) is provided including the computational cost. The proposed models are enhanced with a modified collocation scheme with offsets to Greville abscissae to avoid placing collocation points at the corners. Placing collocation points on smooth surface enables accurate evaluation of normals for BM formulation in addition to straightforward prediction of jump-terms and avoids singularities in $\mathcal{O} (1/r)$ integrals eliminating the need for polar integration. Furthermore, no additional special treatment is required for the hyper-singular integral while collocating on highly distorted elements, such as those containing sphere poles. The obtained results indicate that, CBIE with PSO is a feasible alternative (except for a small number of fictitious frequencies) which is easier to implement. Furthermore, BM presents an outstanding treatment of the complicated geometry of mufflers with internal extended inlet/outlet tube as an interior 3D Helmholtz acoustic problem instead of using mixed or dual BEM.
Revisiting vernacular technique: Engineering a low environmental impact earth stabilisation method
(2022)
The major drawbacks of earth as a construction material — such as its low water stability and moderate strength — have led mankind to stabilize earth. Different civilizations developed vernacular techniques mainly focussing on lime, pozzolan or gypsum stabilization. Recently, cement has become the most commonly used additive in earth stabilization as it improves the strength and durability of plain earth. Also, it is a familiar and globally available construction material. However, using cement as an additive reduces the environmental advantages of earth and run counter to global targets regarding the reduction of CO2 emissions. Alternatives to cement stabilization are currently neither efficient enough to reduce its environmental impact nor allow the possibility of obtaining better results than those of cement. As such, this thesis deals with the rediscovery of a reverse engineering approach for a low environmental impact earth stabilization technique, aiming to replace cement in earth stabilization.
The first step in the method consists in a comprehensive review of earth stabilization with regards to earthen building standards and soil classification, which allows us to identify the research gap. The review showed that there is great potential in using other additives which result in similar improvements as those achieved by cement. However, the studies that have been conducted so far either use expansive soils, which are not suitable for earth constructions or artificial pozzolans that indirectly contribute to CO2 emissions. This is the main research gap.
The key concept for the development in the second step of the method is to combine vernacular additives to both improve the strength and durability of plain earth and to reduce the CO2 emissions. Various earth-mixtures were prepared and both development and performance tests were done to investigate the performance of this technique. The laboratory analyses on mix-design have proven a high durability and the results show a remarkable increase in strength performance. Furthermore, a significant reduction in CO2 emissions in comparison to cement stabilization could be shown.
The third step of the method discusses the results drawn from the experimental programme. In addition, the potential of the new earth mixture with regards to its usability in the field of building construction and architectural design is further elaborated on.
The method used in this study is the first of its kind that allows investors to avoid the very time-consuming processes such as finding a suitable source for soil excavation and soil classification. The developed mixture has significant workability and suitability for production of stabilized earthen panels — the very first of its kind. Such a panel is practically feasible, reasonable, and could be integrated into earthen building standards in general and in particular to DIN 18948, which is related to earthen boards and published in 2018.
The modern industries of the 19th and 20th centuries had multiple effects on the spatial transformation of cities and regions. The past decade has witnessed increasing scholarly and governmental attempts toward conserving modern industrial heritage in the so-called Global North, with the goal, among others, of leveraging this heritage as a driver for urban economic development. In Egypt, the process continues to lag behind; on the one hand, this is due to the perplexing official recognition of the (in)tangible witnesses of modern industries. On the other hand, the official recognition and previous publications focus predominantly on weighing the significance of industrial structures based on their monumental architectural aesthetics. Their historical urban role and spatial attributes as part of urban heritage have yet to be seriously acknowledged. Accordingly, this hinders the integration of the extant industrial sites into the broader debate surrounding urban conservation, leaving them vulnerable to decay and destruction.
This dissertation steers away from the singular investigation of selective modern industrial sites to recall their historical spatial development on a city scale. This is effected by investigating a case study - the Egyptian port city of Alexandria. With the limited secondary data available on modern industries in Alexandria, this dissertation relied predominantly on primary sources. The author collected and leveraged both quantitative and qualitative data to recontextualize modern industries in terms of their spatial dynamics, order, and rationale within cities’ transformation.
By recalling historical spatial development in Alexandria, the contribution of this dissertation lies in highlighting what the author refers to as the Omitted Heritage. This is defined by the modern industries in Egypt that are intentionally, unintentionally, and forgetfully excluded in terms of physical documentation, evaluation, appreciation, and integration within urban development plans. The method used excavated the richness of the established modern industries in Alexandria in terms of their quantity and diversity, which would have otherwise remained largely forgotten. The contextualization of modern industries unveiled spatial periodization, spatial dynamics, and conceptual development. The study draws on important analytical aspects that transcend the sites’ boundaries, elevating their significance to the municipal, regional, national, and even global levels. Its recommendations for further research are also divided into those levels.
In this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with the method of weighed residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. The implementation in this paper is focused on linear elastic solids for sake of conciseness through the NOM can handle more complex nonlinear problems. The NOM can be very flexible and efficient to solve partial differential equations (PDEs), it’s also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Finally, we present some classical benchmark problems including the classical cantilever beam and plate-with-a-hole problem, and we also make an extension of this method to solve complicated problems including phase-field fracture modeling and gradient elasticity material.
In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as ’classical’ approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher order continuous, which is exploited for thin plate analysis that requires C1 continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for the time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.
Material failure can be tackled by so-called nonlocal models, which introduce an intrinsic length scale into the formulation and, in the case of material failure, restore the well-posedness of the underlying boundary value problem or initial boundary value problem. Among nonlocal models, peridynamics (PD) has attracted a lot of attention as it allows the natural transition from continuum to discontinue and thus allows modeling of discrete cracks without the need to describe and track the crack topology, which has been a major obstacle in traditional discrete crack approaches. This is achieved by replacing the divergence of the Cauchy stress tensor through an integral over so-called bond forces, which account for the interaction of particles. A quasi-continuum approach is then used to calibrate the material parameters of the bond forces, i.e., equating the PD energy with the energy of a continuum. One major issue for the application of PD to general complex problems is that they are limited to fairly simple material behavior and pure mechanical problems based on explicit time integration. PD has been extended to other applications but losing simultaneously its simplicity and ease in modeling material failure. Furthermore, conventional PD suffers from instability and hourglass modes that require stabilization. It also requires the use of constant horizon sizes, which drastically reduces its computational efficiency. The latter issue was resolved by the so-called dual-horizon peridynamics (DH-PD) formulation and the introduction of the duality of horizons.
Within the nonlocal operator method (NOM), the concept of nonlocality is further extended and can be considered a generalization of DH-PD. Combined with the energy functionals of various physical models, the nonlocal forms based on the dual-support concept can be derived. In addition, the variation of the energy functional allows implicit formulations of the nonlocal theory. While traditional integral equations are formulated in an integral domain, the dual-support approaches are based on dual integral domains. One prominent feature of NOM is its compatibility with variational and weighted residual methods. The NOM yields a direct numerical implementation based on the weighted residual method for many physical problems without the need for shape functions. Only the definition of the energy or boundary value problem is needed to drastically facilitate the implementation. The nonlocal operator plays an equivalent role to the derivatives of the shape functions in meshless methods and finite element methods (FEM). Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease by a series of matrix multiplications. In addition, NOM can be used to derive many nonlocal models in strong form.
The principal contributions of this dissertation are the implementation and application of NOM, and also the development of approaches for dealing with fractures within the NOM, mostly for dynamic fractures. The primary coverage and results of the dissertation are as follows:
-The first/higher-order implicit NOM and explicit NOM, including a detailed description of the implementation, are presented. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combining with the method of weighted residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. For the sake of conciseness, the implementation in this chapter is focused on linear elastic solids only, though the NOM can handle more complex nonlinear problems. An explicit nonlocal operator method for the dynamic analysis of elasticity solid problems is also presented. The explicit NOM avoids the calculation of the tangent stiffness matrix as in the implicit NOM model. The explicit scheme comprises the Verlet-velocity algorithm. The NOM can be very flexible and efficient for solving partial differential equations (PDEs). It's also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Several numerical examples are presented to show the capabilities of this method.
-A nonlocal operator method for the dynamic analysis of (thin) Kirchhoff plates is proposed. The nonlocal Hessian operator is derived from a second-order Taylor series expansion. NOM is higher-order continuous, which is exploited for thin plate analysis that requires $C^1$ continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.
-A nonlocal fracture modeling is developed and applied to the simulation of quasi-static and dynamic fractures using the NOM. The phase field's nonlocal weak and associated strong forms are derived from a variational principle. The NOM requires only the definition of energy. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems, while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.
We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.
In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems.
Compactly, this thesis encompasses two major parts to examine mechanical responses of polymer compounds and two dimensional materials:
1- Molecular dynamics approach is investigated to study transverse impact behavior of polymers, polymer compounds and two dimensional materials.
2- Large deflection of circular and rectangular membranes is examined by employing continuum mechanics approach.
Two dimensional materials (2D), including, Graphene and molybdenum disulfide (MoS2), exhibited new and promising physical and chemical properties, opening new opportunities to be utilized alone or to enhance the performance of conventional materials. These 2D materials have attracted tremendous attention owing to their outstanding physical properties, especially concerning transverse impact loading.
Polymers, with the backbone of carbon (organic polymers) or do not include carbon atoms in the backbone (inorganic polymers) like polydimethylsiloxane (PDMS), have extraordinary characteristics particularly their flexibility leads to various easy ways of forming and casting. These simple shape processing label polymers as an excellent material often used as a matrix in composites (polymer compounds).
In this PhD work, Classical Molecular Dynamics (MD) is implemented to calculate transverse impact loading of 2D materials as well as polymer compounds reinforced with graphene sheets. In particular, MD was adopted to investigate perforation of the target and impact resistance force . By employing MD approach, the minimum velocity of the projectile that could create perforation and passes through the target is obtained. The largest investigation was focused on how graphene could enhance the impact properties of the compound. Also the purpose of this work was to discover the effect of the atomic arrangement of 2D materials on the impact problem. To this aim, the impact properties of two different 2D materials, graphene and MoS2, are studied. The simulation of chemical functionalization was carried out systematically, either with covalently bonded molecules or with non-bonded ones, focusing the following efforts on the covalently bounded species, revealed as the most efficient linkers.
To study transverse impact behavior by using classical MD approach , Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software, that is well-known among most researchers, is employed. The simulation is done through predefined commands in LAMMPS. Generally these commands (atom style, pair style, angle style, dihedral style, improper style, kspace style, read data, fix, run, compute and so on) are used to simulate and run the model for the desired outputs. Depends on the particles and model types, suitable inter-atomic potentials (force fields) are considered. The ensembles, constraints and boundary conditions are applied depends upon the problem definition. To do so, atomic creation is needed. Python codes are developed to generate particles which explain atomic arrangement of each model. Each atomic arrangement introduced separately to LAMMPS for simulation. After applying constraints and boundary conditions, LAMMPS also include integrators like velocity-Verlet integrator or Brownian dynamics or other types of integrator to run the simulation and finally the outputs are emerged. The outputs are inspected carefully to appreciate the natural behavior of the problem. Appreciation of natural properties of the materials assist us to design new applicable materials.
In investigation on the large deflection of circular and rectangular membranes, which is related to the second part of this thesis, continuum mechanics approach is implemented. Nonlinear Föppl membrane theory, which carefully release nonlinear governing equations of motion, is considered to establish the non-linear partial differential equilibrium equations of the membranes under distributed and centric point loads. The Galerkin and energy methods are utilized to solve non-linear partial differential equilibrium equations of circular and rectangular plates respectively. Maximum deflection as well as stress through the film region, which are kinds of issue in many industrial applications, are obtained.
The computational costs of newly developed numerical simulation play a critical role in their acceptance within both academic use and industrial employment. Normally, the refinement of a method in the area of interest reduces the computational cost. This is unfortunately not true for most nonlocal simulation, since refinement typically increases the size of the material point neighborhood. Reducing the discretization size while keep- ing the neighborhood size will often require extra consideration. Peridy- namic (PD) is a newly developed numerical method with nonlocal nature. Its straightforward integral form equation of motion allows simulating dy- namic problems without any extra consideration required. The formation of crack and its propagation is known as natural to peridynamic. This means that discontinuity is a result of the simulation and does not demand any post-processing. As with other nonlocal methods, PD is considered an expensive method. The refinement of the nodal spacing while keeping the neighborhood size (i.e., horizon radius) constant, emerges to several nonphysical phenomena.
This research aims to reduce the peridynamic computational and imple- mentation costs. A novel refinement approach is introduced. The pro- posed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains (with no intersections) to the nodes of the refinement zone. It will be shown that no ghost forces will be created when changing the horizon sizes in both subdomains. The approach is applied to both bond-based and state-based peridynamic and verified for a simple wave propagation refinement problem illustrating the efficiency of the method. Further development of the method for higher dimensions proves to have a direct relationship with the mesh sensitivity of the PD. A method for solving the mesh sensitivity of the PD is intro- duced. The application of the method will be examined by solving a crack propagation problem similar to those reported in the literature.
New software architecture is proposed considering both academic and in- dustrial use. The available simulation tools for employing PD will be collected, and their advantages and drawbacks will be addressed. The challenges of implementing any node base nonlocal methods while max- imizing the software flexibility to further development and modification
will be discussed and addressed. A software named Relation-Based Sim- ulator (RBS) is developed for examining the proposed architecture. The exceptional capabilities of RBS will be explored by simulating three dis- tinguished models. RBS is available publicly and open to further develop- ment. The industrial acceptance of the RBS will be tested by targeting its performance on one Mac and two Linux distributions.