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The paper aims to research the applications of topological geometry to the architectural concept design process and their combination with the modern digital technology to find novel architectural spaces and forms which are dynamic, easily adaptable to the context and surroundings.

The article uses the method of studying the existing literature on topological geometry and architectural design theory including design thinking, architectural design methods and architectural compositions to analyze and compare them with architectural practices and suggest new topological design tools and methods. Moreover, the paper tests the proposals with a number of preliminary design research experiments. In addition, graphic design software, parametric design, building information modeling (BIM) and digital development trends in architecture were explored and experienced to reveal the application potential of topological design thinking and methods in the trend of architectural digitization.

The paper has analyzed, synthesized and systematized the basic theories of topological geometry in order to clarify their applications in the architectural concept design process. On that basis, the paper proposes a novel topological design thinking and method for finding rich diversified architectural ideas and forms based on original invariant design constraints. Finally, the paper clarifies the combination as well as the mutual, motivating relationship between topological geometry and modern digital technologies when applied to architectural design.

The research contributes a novel design thinking and method based on topological geometry combined with modern digital technology to the architectural design theory. It will be a valuable tool capable of suggesting architects how to think and innovate in architecture in the era of industrial revolution 4.0.

The optimal material microstructures in pure material design are no longer efficient or optimal when accounting macroscopic structure performance with specific boundary conditions. Therefore, it is important to provide a novel multiscale topology optimization framework to tailor the topology of structure and the material to achieve specific applications. In comparison with porous materials, composites consisting of two or more phase materials are more attractive and advantageous from the perspective of engineering application. This paper aims to provide a novel concurrent topological design of structures and microscopic materials for thermal conductivity involving multi-material topology optimization (material distribution) at the lower scale.

In this work, the effective thermal conductivity properties of microscopic three or more phase materials are obtained via homogenization theory, which serves as a bridge of the macrostructure and the periodic material microstructures. The optimization problem, including the topological design of macrostructures and inverse homogenization of microscopic materials, are solved by bi-directional evolutionary structure optimization method.

As a result, the presented framework shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid macrostructures and material microstructures are obtained in terms of optimal thermal conductive path, which verify the effectiveness of the proposed mutliscale topology optimization method. Numerical examples adequately consider effects of initial guesses of the representative unit cell and of the volume constraints of adopted base materials at the microscopic scale on the final design. The resultant structures at both the scales with clear and distinctive boundary between different phases, making the manufacturing straightforward.

This paper presents a novel multiscale concurrent topology optimization method for structures and the underlying multi-phase materials for thermal conductivity. The authors have carried out the concurrent multi-phase topology optimization for both 2D and 3D cases, which makes this work distinguished from existing references. In addition, some interesting and efficient multi-phase material microstructures and macrostructures have been obtained in terms of optimal thermal conductive path.

One of the neglected roles of experiment is the creation of phenomena which then become the centrepiece of theory. The belief that seminal experiments in architectural design must now be reclassified to represent genuine paradigms of “created phenomena” is discussed. The remedy suggested is their analysis, critical evaluation and scrutiny of seminal texts to open the way for the development of topological approaches to design and extension of cybernetics into the field of architecture and construction.

The purpose of this study is to obtain a titanium mandibular implant that possesses a personalized external shape for appearance recovery, a supporting structure for physiological loading and numerous micro-pores for accelerating osseointegration.

A three-dimensional intact mandibular model of a beagle dog was created from cone-beam computerized tomography scans. A segment of the lower jaw bone was resected and replaced by a personalized implant with comprehensive structures including a customized external shape, supporting structures and micro-pores, which were designed by topology optimization. Then with FEM analysis, the stress, displacement distribution and compliance of the designed implant were compared with the non-optimized model. The weight of the optimized implant that was fabricated by SLM with titanium alloy powder was measured and contrasted with the predicted non-optimized model for evaluating the viability of the design.

The FEM results showed the peaks of von Mises stress and displacement on the optimized implant were much lower than those of the implant without optimization. With topology optimization, the compliance of the implant decreased significantly by 53.3 per cent, and a weight reduction of 37.2 per cent could be noticed.

A design strategy for personalized implant, with comprehensive structures and SLM as the fabrication method, has been developed and validated by taking a canine mandible as the case study. With comprehensive structures, the implant presented good biomechanical behaviors thanks to the most appropriate supporting structures obtained by optimal design. The topological optimal design combined with SLM printing proved to be an effective method for the design and fabrication of personalized implant with complex structures.

Robust design is very important for manufacturers to ensure the quality of the finished product. Therefore, a robustness measure is needed for the topological design of electromagnetic problems which may be sensitive to parameter variations. The purpose of this paper is to propose a robust objective function for topological design problems.

In this paper, a robust objective function for topology optimization is defined on an uncertainty set using the worst case analysis. The robustness of a topological design is defined as the worst response due to the variations of the location of the topology change. The approach is based on the definition of a topological gradient.

The robust topology optimization (RTO) was applied to eddy current crack reconstruction problems. The numerical applications showed that this method can provide more reliable results for the reconstruction in the presence of significant noise in the measured signal.

The RTO may be applied to some more complicated design problems; however large computational costs may result.

This paper has defined a robustness metric for topology design and a robust design model is proposed for topology optimization problems.

The purpose of this study is to solve the inverse homogenization problem, or so-called material design problem, using the topological derivative concept.

The optimal topology is obtained through a relaxed formulation of the problem by replacing the characteristic function with a continuous design variable, so-called density variable. The constitutive tensor is then parametrized with the density variable through an analytical interpolation scheme that is based on the topological derivative concept. The intermediate values that may appear in the optimal topologies are removed by penalizing the perimeter functional.

The optimization process benefits from the intermediate values that provide the proposed method reaching to solutions that the topological derivative had not been able to find before. In addition, the presented theory opens the path to propose a new framework of research where the topological derivative uses classical optimization algorithms.

The proposed methodology allows us to use the topological derivative concept for solving the inverse homogenization problem and to fulfil the optimality conditions of the problem with the use of classical optimization algorithms. The authors solved several material design examples through a projected gradient algorithm to show the advantages of the proposed method.

This work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.

The resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.

The description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.

The original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

The purpose of this paper is to present applications of the topological optimization method dealing with fluid dynamic problems in two- and three dimensions. The main goal is to develop a tool package able to optimize topology in realistic devices (e.g. inlet manifolds) considering the non-linear terms on Navier–Stokes equations.

Using an in-house Fortran code, a Galerkin stabilized finite element is implemented method to solve the three equation systems necessary for the topological optimization method: the direct problem, adjoint problem and topological derivative. The authors address the non-linearity in the equations using an iterative method. Different techniques to create holes into a two-dimensional discrete domain are analyzed.

One technique to create holes produces more accurate and robust results. The authors present several examples of applications in two- and three-dimensional components, which highlight the potential of this method in the optimization of fluid components.

The authors contribute to the methodology and design in engineering.

Engineering fluid flow systems are used in many different industrial applications, e.g. oil flow in pipes; air flow around an airplane wing; sailing submarines; blood flow in synthetic arteries; and thermal and fissure spreading problems. The aim of this work is to create an effective design tool for obtaining efficient engineering structures and devices.

The authors contribute by creating an application of the method to design a tridimensional realistic device, which can be essayed experimentally. Particularly, the authors apply the design tool to an inlet manifold.

The purpose of this paper is to establish and implement a direct topological reanalysis algorithm for general successive structural modifications, based on the updating matrix triangular factorization (UMTF) method for non-topological modification proposed by Song et al. [Computers and Structures, 143(2014):60-72].

In this method, topological modifications are viewed as a union of symbolic and numerical change of structural matrices. The numerical part is dealt with UMTF by directly updating the matrix triangular factors. For symbolic change, an integral structure which consists of all potential nodes/elements is introduced to avoid side effects on the efficiency during successive modifications. Necessary pre- and post processing are also developed for memory-economic matrix manipulation.

The new reanalysis algorithm is applicable to successive general structural modifications for arbitrary modification amplitudes and locations. It explicitly updates the factor matrices of the modified structure and thus guarantees the accuracy as full direct analysis while greatly enhancing the efficiency.

Examples including evolutionary structural optimization and sequential construction analysis show the capability and efficiency of the algorithm.

This innovative paper makes direct topological reanalysis be applicable for successive structural modifications in many different areas.

A robotic wheelchair system was designed to assist disabled people with disabilities to walk.

An anticipated sharing control strategy based on topological map is proposed in this paper, which is used to assist robotic wheelchairs to realize interactive navigation. Then, a robotic wheelchair navigation control system based on the brain-computer interface and topological map was designed and implemented.

In the field of robotic wheelchairs, the problems of poor use, narrow application range and low humanization are still not improved.

In the system, the topological map construction is not restricted by the environment structure, which helps to expand the scope of application; the shared control system can predict the users’ intention and replace the users’ decision to realize human-machine interactive navigation, which has higher security, robustness and comfort.