Search results
1 – 10 of over 2000Phillip Baumann and Kevin Sturm
The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological…
Abstract
Purpose
The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals.
Design/methodology/approach
The authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model.
Findings
The authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method.
Originality/value
In contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.
Details
Keywords
Lalaina Rakotondrainibe, Grégoire Allaire and Patrick Orval
This paper is devoted to the theoretical and numerical study of a new topological sensitivity concerning the insertion of a small bolt connecting two parts in a mechanical…
Abstract
Purpose
This paper is devoted to the theoretical and numerical study of a new topological sensitivity concerning the insertion of a small bolt connecting two parts in a mechanical structure. First, an idealized model of bolt is proposed which relies on a non-local interaction between the two ends of the bolt (head and threads) and possibly featuring a pre-stressed state. Second, a formula for the topological sensitivity of such an idealized bolt is rigorously derived for a large class of objective functions. Third, numerical tests are performed in 2D and 3D to assess the efficiency of the bolt topological sensitivity in the case of no pre-stress. In particular, the placement of bolts (acting then as springs) is coupled to the further optimization of their location and to the shape and topology of the structure for volume minimization under compliance constraint.
Design/methodology/approach
The methodology relies on the adjoint method and the variational formulation of the linearized elasticity equations in order to establish the topological sensitivity.
Findings
The numerical results prove the influence of the number and locations of the bolts which strongly influence the final optimized design of the structure.
Originality/value
This paper is the first one to study the topology optimization of bolted systems without a fixed prescribed number of bolts.
Details
Keywords
Seyed Ashkan Zarghami and Indra Gunawan
As a response to the growing operational and disruptive threats to water distribution networks (WDNs), researchers have developed a vast array of methods for the reliability…
Abstract
Purpose
As a response to the growing operational and disruptive threats to water distribution networks (WDNs), researchers have developed a vast array of methods for the reliability analysis of WDNs. In order to follow this growing number of methods, this paper reviews and documents in one place the historical developments in the reliability analysis of WDN.
Design/methodology/approach
A systematic literature review (SLR) is carried out to summarize the state-of-the-art research on reliability analysis of WDNs. In conducting this systemic literature review, the authors adopted an iterative approach to define appropriate keywords, analyze and synthesize data and finalizing the classification results.
Findings
First, the hydraulic approach to reliability analysis is currently pervasive, and relatively little academic research has addressed the topological reliability analysis of WDNs. Second, in order to provide a comprehensive picture of the network reliability, a different approach that integrates topological and hydraulic attributes seems a more effective method. Third, the conventional reliability analysis methods are only effective for demonstrating a snapshot of these networks at a given point in time. The availability of methods that enable researchers to evaluate the reliability in response to changes in its variables is still a major challenge.
Originality/value
The present paper facilitates future research in the reliability analysis of WDNs by providing a source of references for researchers and water utilities. Further, this article makes a contribution to the literature by offering a roadmap for future reliability analysis of WDNs by reviewing the evolution of the current reliability analysis methods throughout history.
Details
Keywords
Frédérique Le Louër and María-Luisa Rapún
The purpose of this paper is to revisit the recursive computation of closed-form expressions for the topological derivative of shape functionals in the context of time-harmonic…
Abstract
Purpose
The purpose of this paper is to revisit the recursive computation of closed-form expressions for the topological derivative of shape functionals in the context of time-harmonic acoustic waves scattering by sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions).
Design/methodology/approach
The elliptic boundary value problems in the singularly perturbed domains are equivalently reduced to couples of boundary integral equations with unknown densities given by boundary traces. In the case of circular or spherical holes, the spectral Fourier and Mie series expansions of the potential operators are used to derive the first-order term in the asymptotic expansion of the boundary traces for the solution to the two- and three-dimensional perturbed problems.
Findings
As the shape gradients of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.
Originality/value
The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function in the iterated numerical solution of any shape optimization or imaging problem relying on time-harmonic acoustic waves propagation. When coupled with converging Gauss−Newton iterations for the search of optimal boundary parametrizations, it generates fully automatic algorithms.
Details
Keywords
The purpose of this paper is to combine both Crime Prevention Through Environmental Design (CPTED) and space syntax for the more detailed and overall analysis of built environment…
Abstract
Purpose
The purpose of this paper is to combine both Crime Prevention Through Environmental Design (CPTED) and space syntax for the more detailed and overall analysis of built environment in terms of crime. The author is aiming to verify the designed research methodology by its application in cities that are similar in terms of size and population, and are very different in culture and location: New Haven (USA) and Kaunas (Lithuania).
Design/methodology/approach
Based on CPTED strategies the factors of urban environment are analyzed, such as topological depth from private space to a public space, density of entrances and windows, street’s constitutedness, inter-visibility, land use, blind walls, segment’s accessibility, greenery, lighting, objects of small architecture, graffiti. Space syntax method is applied for the analysis of the following topological properties of urban spaces: integration, choice, depth, connectivity.
Findings
The combination of both methods revels that choice and depth of urban spaces are related to robberies, and connectivity and depth are related to thefts from motor vehicles in New Haven. Integration and depth are related to thefts from motor vehicles in Kaunas. According to the correlation analysis results, in Kaunas more robberies happen in common use areas, and more thefts from cars happen in the spaces with blind walls and dense abandoned greenery. In New Haven more thefts from motor vehicles happen in spaces with blind walls. In both cities with the increase of the topological depth the thefts from motor vehicles increase too.
Originality/value
Based on the research results recommendations on urban planning and design are developed. The implementation of the recommendations might make New Haven and Kaunas safer.
Details
Keywords
Lucas Fernandez and Ravi Prakash
The purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.
Abstract
Purpose
The purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.
Design/methodology/approach
The method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.
Findings
In this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.
Originality/value
The current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.
Details
Keywords
Liang Liu, Bin Chen, Wangchun Jiang, Lingnan He and Xiaogang Qiu
WeChat is the largest acquaintance social networking platform in China, in which users can view and reshare web pages shared by friends. This paper aims to analyze the…
Abstract
Purpose
WeChat is the largest acquaintance social networking platform in China, in which users can view and reshare web pages shared by friends. This paper aims to analyze the spatio-temporal dynamics of web pages diffused in WeChat and advice on commercials.
Design/methodology/approach
A large number of web pages diffused in WeChat are collected and exclusively divided into four categories according to their titles, including advertisements, news bulletins, holiday greetings and emotional essays. For each web page, an information cascade (tree structure) is constructed to describe the diffusion trace. Based on the categories, the spatio-temporal popularity is characterized; the topological, temporal and spatial properties are examined; and the spatio-temporal diffusion velocity is explored.
Findings
Through comparative analysis, different categories of pages show diversity. For spatio-temporal popularity, there is no significant difference in cascade size; holiday greetings usually last for a relatively short time on average; emotional essays are more likely to spread to more provinces. For topological, temporal and spatial characteristics, the diffusion process of advertisements is more likely to be broadcasting than other categories; news bulletins and holiday greetings have an obvious bursty; the number of viewing behavior decreases from east to west in general. For spatio-temporal diffusion velocity, emotional essays diffuse the fastest in topological and spatio-temporal dimensions.
Originality/value
These findings contribute to promoting products and providing support for data driven modeling of information diffusion and human activity in spatio-temporal dimensions.
Details
Keywords
Frédérique Le Louër and María-Luisa Rapún
In this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional…
Abstract
Purpose
In this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.
Design/methodology/approach
From the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.
Findings
As the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.
Originality/value
The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.
Details
Keywords
Farzad Shafiei Dizaji and Mehrdad Shafiei Dizaji
The purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one…
Abstract
Purpose
The purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one of the sources of errors. In numerical analysis, sometimes handling numerical errors is challenging. However, by applying appropriate algorithms, these errors are manageable and can be reduced. In this study, five novel topological algorithms were proposed in setting up a structural flexibility matrix, and five different examples were used in applying the proposed algorithms. In doing so round-off errors were reduced remarkably.
Design/methodology/approach
Five new algorithms were proposed in order to optimize the conditioning of structural matrices. Along with decreasing the size and duration of analyses, minimizing analytical errors is a critical factor in the optimal computer analysis of skeletal structures. Appropriate matrices with a greater number of zeros (sparse), a well structure and a well condition are advantageous for this objective. As a result, a problem of optimization with various goals will be addressed. This study seeks to minimize analytical errors such as rounding errors in skeletal structural flexibility matrixes via the use of more consistent and appropriate mathematical methods. These errors become more pronounced in particular designs with ill-suited flexibility matrixes; structures with varying stiffness are a frequent example of this. Due to the usage of weak elements, the flexibility matrix has a large number of non-diagonal terms, resulting in analytical errors. In numerical analysis, the ill-condition of a matrix may be resolved by moving or substituting rows; this study examined the definition and execution of these modifications prior to creating the flexibility matrix. Simple topological and algebraic features have been mostly utilized in this study to find fundamental cycle bases with particular characteristics. In conclusion, appropriately conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.
Findings
(1) Five new algorithms were proposed in order to optimize the conditioning of structural flexibility matrices. (2) A JAVA programming language was written for all five algorithms and a friendly GUI software tool is developed to visualize sub-optimal cycle bases. (3) Topological and algebraic features of the structures were utilized in this study.
Research limitations/implications
This is a multi-objective optimization problem which means that sparsity and well conditioning of a matrix cannot be optimized simultaneously. In conclusion, well-conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.
Practical implications
Engineers always finding mathematical modeling of real-world problems and make them as simple as possible. In doing so, lots of errors will be created and these errors could cause the mathematical models useless. Applying decent algorithms could make the mathematical model as precise as possible.
Social implications
Errors in numerical simulations should reduce due to the fact that they are toxic for real-world applications and problems.
Originality/value
This is an original research. This paper proposes five novel topological mathematical algorithms in order to optimize the structural flexibility matrix.
Details
Keywords
Yanchuang Cao, Junjie Rong, Lihua Wen and Jinyou Xiao
The purpose of this paper is to develop an easy-to-implement and accurate fast boundary element method (BEM) for solving large-scale elastodynamic problems in frequency and time…
Abstract
Purpose
The purpose of this paper is to develop an easy-to-implement and accurate fast boundary element method (BEM) for solving large-scale elastodynamic problems in frequency and time domains.
Design/methodology/approach
A newly developed kernel-independent fast multipole method (KIFMM) is applied to accelerating the evaluation of displacements, strains and stresses in frequency domain elastodynamic BEM analysis, in which the far-field interactions are evaluated efficiently utilizing equivalent densities and check potentials. Although there are six boundary integrals with unique kernel functions, by using the elastic theory, the authors managed to accelerate these six boundary integrals by KIFMM with the same kind of equivalent densities and check potentials. The boundary integral equations are discretized by Nyström method with curved quadratic elements. The method is further used to conduct the time-domain analysis by using the frequency-domain approach.
Findings
Numerical results show that by the fast BEM, high accuracy can be achieved and the computational complexity is brought down to linear. The performance of the present method is further demonstrated by large-scale simulations with more than two millions of unknowns in the frequency domain and one million of unknowns in the time domain. Besides, the method is applied to the topological derivatives for solving elastodynamic inverse problems.
Originality/value
An efficient KIFMM is implemented in the acceleration of the elastodynamic BEM. Combining with the Nyström discretization based on quadratic elements and the frequency-domain approach, an accurate and highly efficient fast BEM is achieved for large-scale elastodynamic frequency domain analysis and time-domain analysis.
Details