Under Review

Under Review.

Natural tissues are incorporated with vasculature, which is further integrated with a cardiovascular system responsible for driving perfusion of nutrient-rich oxygenated blood through the vasculature to support cell metabolism within most cell-dense tissues. Since scaffold-free biofabricated tissues being developed into clinical implants, research models, and pharmaceutical testing platforms should similarly exhibit perfused tissue-like structures, we generated a generalizable biofabrication method resulting in self-supporting perfused (SSuPer) tissue constructs incorporated with perfusible microchannels and integrated with the modular FABRICA perfusion bioreactor. As proof of concept, we perfused an MLO-A5 osteoblast-based SSuPer tissue in the FABRICA. Although our resulting SSuPer tissue replicated vascularization and perfusion observed in situ, supported its own weight, and stained positively for mineral using Von Kossa staining, our in vitro results indicated that computational fluid dynamics (CFD) should be used to drive future construct design and flow application before further tissue biofabrication and perfusion. We built a CFD model of the SSuPer tissue integrated in the FABRICA and analyzed flow characteristics (net force, pressure distribution, shear stress, and oxygen distribution) through five SSuPer tissue microchannel patterns in two flow directions and at increasing flow rates. Important flow parameters include flow direction, fully developed flow, and tissue microchannel diameters matched and aligned with bioreactor flow channels. We observed that the SSuPer tissue platform is capable of providing direct perfusion to tissue constructs and proper culture conditions (oxygenation, with controllable shear and flow rates), indicating that our approach can be used to biofabricate tissue representing primary tissues and that we can model the system in silico.

This work introduces a cluster-based structural optimization (CBSO) method for the design of categorical multimaterial structures subjected to crushing, dynamic loading. The proposed method consists of three steps: conceptual design generation, design clustering, and Bayesian optimization. In the first step, a conceptual design is generated using the hybrid cellular automaton (HCA) algorithm. In the second step, threshold-based cluster analysis yields a lower-dimensional design. Here, a cluster validity index for structural optimization is introduced in order to qualitatively evaluate the clustered design. In the third step, the optimal design is obtained through Bayesian optimization, minimizing a constrained expected improvement function. This function allows to impose soft constraints by properly redefining the expected improvement based on the maximum constraint violation. The Bayesian optimization algorithm implemented in this work has the ability to search over (i) a real design space for sizing optimization, (ii) a categorical design space for material selection, or (iii) a mixed design space for concurrent sizing optimization and material selection. With the proposed method, materials are optimally selected based on multiple attributes and multiple objectives without the need for material ranking. The effectiveness of this approach is demonstrated with the design for crashworthiness of multimaterial plates and thin-walled structures

Purpose – This paper aims to establish a multiscale topology optimization method for the optimal design of non-periodic, self-supporting cellular structures subjected to thermo-mechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable and suitable for additive manufacturing (AM).
Design/methodology/approach – The proposed method seeks to maximize thermo-mechanical performance at the macroscale in a conceptual design while obtaining maximum shear modulus for each unit cell at the mesoscale. Then, the macroscale performance is re-estimated, and the mesoscale design is updated until the macroscale performance is satisfied.
Findings – A two-dimensional Messerschmitt Bolkow Bolhm (MBB) beam withstanding thermo-mechanical load is presented to illustrate the proposed design method. Furthermore, the method is implemented to optimize a three-dimensional injection mold, which is successfully prototyped using 420 stainless steel infiltrated with bronze.
Originality/value – By developing a computationally efficient and manufacturing friendly inverse homogenization approach, the novel multiscale design could generate porous molds which can save up to 30 per cent material compared to their solid counterpart without decreasing thermomechanical performance.
Practical implications – This study is a useful tool for the designer in molding industries to reduce the cost of the injection mold and take full advantage of AM.

Aluminum foam sandwich (AFS) structures are suitable for impact protection in lightweight structural components due to their specific energy absorption capability under compression. However, tailoring the deformation patterns of the foam cells is a difficult task due to the randomness of their internal architecture. The objective of this study is to analyze the effect of embedding aluminum pins into an AFS panel (Z-pinning) to better control its deformation pattern and improve its energy absorption capability. This study considers a closed-cell AFS panel and analyzes the effect of multi-pin layout parallel to the direction of the uniaxial compressive loading. The results of the experimental tests on the reference (without Z-pinning) AFS are utilized to develop numerical models for the reference and Z-pinned AFS structures. Physical experiments and numerical simulations are carried out to demonstrate the advantages of Z-pinning with aluminum pins. The results exhibit a significant increase in elastic modulus, plateau stress and energy absorption capability of the Z-pinned samples. Also, the effect of the pin size and Z-pinning layout on the mechanical performance of the Z-pinned AFS is also investigated using numerical simulations.

This work introduces a new approach to targeting the dynamic response of thin-walled energy-absorbing structures through the decomposition of the force-displacement (FD) response and the use of topometry (thickness) optimization. The proposed method divides the nonlinear optimization problem into a series of analytical subproblems. In each iteration, an explicit dynamic analysis is carried out and the dynamic response of the structure is then used to define the subproblem. Numerical examples show that the algorithm can tailor the FD response of the structure to a target FD curve. Progressive collapse, which is a high-energy collapse mode and desired in design for crashworthy, is observed in the optimized thin-walled structures. The proposed algorithm is computationally efficient as it uses a fewer explicit simulations to reach the target response.

This paper presents a robust compound control strategy to produce a stable gait in dynamic bipedal robots under random perturbations. The proposed control strategy consists of two interactive loops: an adaptive trajectory generator and a robust trajectory tracking controller. The adaptive trajectory generator produces references for the robot controlled joints without a-priori knowledge of the terrain features and minimizes the effects of disturbances and model uncertainties during the gait, particularly during the support-leg exchange. The trajectory tracking controller is a non-switching robust multivariable generalized proportional integral (GPI) controller. The GPI controller rejects external disturbances and uncertainties faced by the robot during the swing walking phase. The proposed control strategy was evaluated on the numerical model of a five-link planar bipedal robot with one degree of under-actuation, four actuators, and point feet. The results showed robust performance and stability under external disturbances and model parameter uncertainties on uneven terrain with uphills and downhills. The stability of the gait was proven through the computation of a Poincaré return map for a hybrid zero dynamics with uncertainties (HZDU) model, which shows convergence to a bounded neighborhood of a nominal orbital periodic behavior.

This paper presents a disturbance rejection control strategy for hybrid dynamic systems exposed to model uncertainties and external disturbances. The focus of this work is the gait control of dynamic bipedal robots. The proposed control strategy integrates continuous and discrete control actions. The continuous control action uses a novel model-based active disturbance rejection control (ADRC) approach to track gait trajectory references. The discrete control action resets the gait trajectory references after the impact produced by the robot’s support-leg exchange to maintain a zero tracking error. A Poincaré return map is used to search asymptotic stable periodic orbits in an extended hybrid zero dynamics (EHZD). The EHZD reflects a lower-dimensional representation of the full hybrid dynamics with uncertainties and disturbances. A physical bipedal robot testbed, referred to as Saurian, is fabricated for validation purposes. Numerical simulation and physical experiments show the robustness of the proposed control strategy against external disturbances and model uncertainties that affect both the swing motion phase and the support-leg exchange.

The continuous development of sport technologies constantly demands advancements in protective headgear to reduce the risk of head injuries. This article introduces new cellular helmet liner designs through two approaches. The first approach is the study of energy-absorbing biological materials. The second approach is the study of lattices comprised of force-diverting compliant mechanisms. On the one hand, bio-inspired liners are generated through the study of biological, hierarchical materials. An emphasis is given on structures in nature that serve similar concussion-reducing functions as a helmet liner. Inspiration is drawn from organic and skeletal structures. On the other hand, compliant mechanism lattice (CML)-based liners use topology optimization to synthesize rubber cellular unit cells with effective positive and negative Poisson's ratios. Three lattices are designed using different cellular unit cell arrangements, namely, all positive, all negative, and alternating effective Poisson's ratios. The proposed cellular (bio-inspired and CML-based) liners are embedded between two polycarbonate shells, thereby, replacing the traditional expanded polypropylene foam liner used in standard sport helmets. The cellular liners are analyzed through a series of 2D extruded ballistic impact simulations to determine the best performing liner topology and its corresponding rubber hardness. The cellular design with the best performance is compared against an expanded polypropylene foam liner in a 3D simulation to appraise its protection capabilities and verify that the 2D extruded design simulations scale to an effective 3D design.

The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a clusterbased structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models.

An emerging approach in biofabrication is the creation of 3D tissue constructs through scaffold-free, cell spheroid-only methods. The basic mechanism in this technology is spheroid fusion, which is driven by the minimization of energy, the same biophysical mechanism that governs spheroid formation. However, other factors such as oxygen and metabolite accessibility within spheroids impact on spheroid properties and their ability to form larger-scale structures. The goal of our work is to develop a simulation platform eventually capable of predicting the conditions that minimize metabolism-related cell loss within spheroids. To describe the behavior and dynamic properties of the cells in response to their neighbors and to transient nutrient concentration fields, we developed a hybrid discrete-continuous heuristic model, combining a cellular Potts-type approach with field equations applied to a randomly populated spheroid cross-section of prescribed cell-type constituency. This model allows for the description of: (i) cellular adhesiveness and motility; (ii) interactions with concentration fields, including diffusivity and oxygen consumption; and (iii) concentration-dependent, stochastic cell dynamics, driven by metabolite-dependent cell death. Our model readily captured the basic steps of spheroid-based biofabrication (as specifically dedicated to scaffold-free bioprinting), including intra-spheroid cell sorting (both in 2D and 3D implementations), spheroid defect closure, and inter-spheroid fusion. Moreover, we found that when hypoxia occurring at the core of the spheroid was set to trigger cell death, this was amplified upon spheroid fusion, but could be mitigated by external oxygen supplementation. In conclusion, optimization and further development of scaffold-free bioprinting techniques could benefit from our computational model which is able to simultaneously account for both cellular dynamics and metabolism in constructs obtained by scaffold-free biofabrication.

This study presents an efficient multimaterial design optimization algorithm that is suitable for nonlinear structures. The proposed algorithm consists of three steps: conceptual design generation, clustering, and metamodel-based global optimization. The conceptual design is generated using a structural optimization algorithm for linear models or a heuristic design algorithm for nonlinear models. Then, the conceptual design is clustered into a predefined number of clusters (materials) using a machine learning algorithm. Finally, the global optimization problem aims to find the optimal material parameters of the clustered design using metamodels. The metamodels are built using sampling and cross-validation and sequentially updated using an expected improvement function until convergence. The proposed methodology is demonstrated using examples from multiple physics and compared with traditional multimaterial topology optimization (MTOP) method. The proposed approach is applied to a nonlinear, multi-objective design problems for crashworthiness.

This work presents a topology optimization approach for lattice structures subjected to thermal and mechanical loads. The focus of this work is the design of injection molds. The proposed approach seeks to minimize the injection mold mass while satisfying constraints on mechanical and thermal performance. The optimal injection molds are characterized by a quasi-periodic distribution of lattice unit cells of variable relative density. The resulting lattice structures are suitable for additive manufacturing. The proposed structural optimization approach uses thermal and mechanical finite element analyses at two length scales: mesoscale and macroscale. At the mesoscale, lattice unit cells are utilized to obtain homogenized thermal and mechanical properties as a function of the lattice relative density. At the macroscale, the lattice unit cells are optimally distributed using the homogenized properties. The proposed design approach is demonstrated through 2D and 3D examples including the optimal design of an injection mold. The optimized injection mold is prototyped using additive manufacturing. The numerical model of the optimized mold shows that, with respect to a traditional solid mold design, a mass reduction of over 30% can be achieved with a small increase in nodal displacement (under 5 microns) and no difference in nodal temperature.

Plastic injection molding is a versatile process and a major part of the present plastic manufacturing industry. Traditional die design is limited to straight (drilled) cooling channels, which don’t impart optimal thermal (or thermo-mechanical) performance. With the advent of additive manufacturing technology, design of injection molding tools with conformal cooling channels is now possible. The incorporation of conformal cooling channels can improve the thermal performance of an injection mold, though it may compromise the structural or mechanical stability of the mold. However, optimum conformal channels based on thermo-mechanical performance are not found in the literature. This paper proposes a design methodology to generate optimized design configurations of such channels in plastic injection molds. Design of experiments (DOEs) technique is used to study the effect of critical design parameters of conformal channels. In addition, a trade-off technique is utilized to obtain optimum design configurations of conformal cooling channels for “best” thermo-mechanical performance of a mold.

This work presents implementation of numerical analysis and topology optimization techniques for redesigning traditional injection molding tools. Traditional injection molding tools have straight cooling channels, drilled into a solid body of the core and cavity. The cooling time constitutes a large portion of the total production cycle that needs to be reduced as much as possible in order to bring in a significant improvement in the overall business of injection molding industry. Incorporating conformal cooling channels in the traditional dies is a highly competent solution to lower the cooling time as well as improve the plastic part quality. In this paper, the thermal and mechanical behavior of cavity and core with conformal cooling channels are analyzed to find an optimum design for molding tools. The proposed design with conformal cooling channels provides a better alternative than traditional die designs with straight channels. This design is further optimized using thermo-mechanical topology optimization based on a multiscale approach for generating sound porous structures. The implemented topology optimization results in a light-weight yet highly effective die cavity and core. The reduction in weight achieved through the design of dies with porous structures is meant to facilitate the adoption of additive manufacturing for die making by the tooling industry.

This work presents a framework for optimizing additive manufacturing of plastic injection molds. The proposed system consists of three modules, namely process and material modeling, multi-scale topology optimization, and experimental testing, calibration and validation. Advanced numerical simulation is implemented for a typical die with conformal cooling channels to predict cycle time, part quality and tooling life. A multi-scale thermo-mechanical topology optimization algorithm is being developed to minimize the die weight and enhance its thermal performance. The technique is implemented for simple shapes for validation before it is applied to dies with conformal cooling in future work. Finally, material modeling using simulation as well as design of experiments is underway for obtaining the material properties and their variations.

This work introduces a design method for the progressive collapse of thin-walled tubular components under axial and oblique impacts. The proposed design method follows the principles of topometry optimization for compliant mechanism design in which the output port location and direction determine the folding (collapse) mode. In this work, the output ports are located near the impact end with a direction that is perpendicular to the component's longitudinal axis. The topometry optimization is achieved with the use of hybrid cellular automata for thin-wall structures. The result is a complex enforced buckle zone design that acts as a triggering mechanism to (a) initiate a specific collapse mode from the impact end, (b) stabilize the collapse process, and (c) reduce the peak force. The enforced buckle zone in the end portion of the tube also helps to avoid or delay the onset of global bending during an oblique impact with load angles higher than a critical value, which otherwise adversely affects the structure's capacity for load-carrying and energy absorption. The proposed design method has the potential to dramatically improve thin-walled component crashworthiness.

The objective of this research is to determine the influence of gear tooth geometrical variations in the performance of a double wave harmonic drive through statistical analysis. This work incorporates state of the art analytical and numerical models to evaluate kinematic error, load capacity, bending fatigue strength, and pitting. The geometric variables considered in this study include gear modulus, pressure angle, and tooth correction factor. The statistical analysis follows a three-level full-factorial design of experiments. Nonlinear dynamic simulation is accompanied by finite element analysis to estimate contact and bending stresses. Largest bending fatigue strength is also determined. Results demonstrate that gear modulus is the geometric parameter with prevalent influence on the kinematic error, and pitting life is rather high for all geometric variables considered.

This paper presents an efficient and compact MATLAB code to solve three-dimensional topology optimization problems. The 169 lines comprising this code include finite element analysis, sensitivity analysis, density filter, optimality criterion optimizer, and display of results. The basic code solves minimum compliance problems. A systematic approach is presented to easily modify the definition of supports and external loads. The paper also includes instructions to define multiple load cases, active and passive elements, continuation strategy, synthesis of compliant mechanisms, and heat conduction problems, as well as the theoretical and numerical elements to implement general non-linear programming strategies such as SQP and MMA. The code is intended for students and newcomers in the topology optimization. The complete code is provided in Appendix C and it can be downloaded from http://top3dapp.com.

The burgeoning growth of tall buildings around the world requires novel design methodologies to resolve design challenges imposed by the enormous volume of material and energy employed during their construction and operation. To meet this upcoming social demand on tall buildings, practical and efficient design method is proposed for optimal outrigger placement using topology optimization. Outriggers, one of the key structural components in a tall and narrow building, are the horizontal structures which connect the building core (spine) and the exterior surface in order to improve the building’s shear stiffness. In the proposed method, the high-fidelity simulation model of a tall building is constructed with multiple finite element types for the core and the reinforcing truss system. The floor-wise outriggers are parameterized using the Simple Isotropic Material with Penalization (SIMP) and defined as the design variables. The outrigger placement problem is solved using topology optimization. The continuation method is used for material penalization parameter in order to obtain “0–1” design. The versatility of the proposed design methodology is proven using the realistic FEM model of a three-dimensional 201 m tall building.

This work presents a novel method for designing crashworthy structures with controlled energy absorption based on the use of compliant mechanisms. This method helps in introducing flexibility at desired locations within the structure, which in turn reduces the peak force at the expense of a reasonable increase in intrusion. For this purpose, the given design domain is divided into two subdomains: flexible (FSD) and stiff (SSD) subdomains. The design in the flexible subdomain is governed by the compliant mechanism synthesis approach for which output ports are defined at the interface between the two subdomains. These output ports aid in defining potential load paths and help the user make better use of a given design space. The design in the stiff subdomain is governed by the principle of a fully-stressed design for which material is distributed to achieve uniform energy distribution within the design space. Together, FSD and SSD provide for a combination of flexibility and stiffness in the structure, which is desirable for most crash applications. Copyright © 2012 by ASME Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal.

The paper presents a work in the field of ‘mixed reality boundaries’ applied to the visualization of museum collections in order to display the collections ‘live’ as a way to extend virtually the preservation areas of museum collections. To achieve this goal, it was set out to integrate several virtual-studio techniques with multicasting IP in the web and the ‘tectonics’ of museums architecture were also redesigned to turn this sort of new infrastructure into what will be a new typology of mixed architectures for museum preservation areas. Dynamic lighting for Chroma-keying techniques were adapted to the real time applications and a MR J3D collision tool was added to the remote motion control of the video camera´s 3d scene live navigation.

This investigation introduces a methodology to design dynamically crushed thin-walled tubular structures for crashworthiness applications. Due to their low cost, high-energy absorption efficiency, and capacity to withstand long strokes, thin-walled tubular structures are extensively used in the automotive industry. Tubular structures subjected to impact loading may undergo three modes of deformation: progressive crushing/buckling, dynamic plastic buckling, and global bending or Euler-type buckling. Of these, progressive buckling is the most desirable mode of collapse because it leads to a desirable deformation characteristic, low peak reaction force, and higher energy absorption efficiency. Progressive buckling is generally observed under pure axial loading; however, during an actual crash event, tubular structures are often subjected to oblique impact loads in which Euler-type buckling is the dominating mode of deformation. This undesired behavior severely reduces the energy absorption capability of the tubular structure. The design methodology presented in this paper relies on the ability of a compliant mechanism to transfer displacement and/or force from an input to desired output port locations. The suitable output port locations are utilized to enforce desired buckle zones, mitigating the natural Euler-type buckling effect. The problem addressed in this investigation is to find the thickness distribution of a thin-walled structure and the output port locations that maximizes the energy absorption while maintaining the peak reaction force at a prescribed limit. The underlying design for thickness distribution follows a uniform mutual potential energy density under a dynamic impact event. Nonlinear explicit finite element code LS-DYNA is used to simulate tubular structures under crash loading. Biologically inspired hybrid cellular automaton (HCA) method is used to drive the design process. Results are demonstrated on long straight and S-rail tubes subject to oblique loading, achieving progressive crushing in most cases.

This paper introduces a control-based optimization algorithm to solve topology optimization problems for structures of minimum compliance. In this approach, the iterative solution process is expressed as a multivariable control system. The elements comprising the structure are numerically incorporated with sensors, controllers, and actuators. The sensors determine a response signal as a function of the problem’s sensitivity coefficients. The controllers minimize the error between this response and a corresponding setpoint obtained from the problem’s optimality conditions. The actuators modify the design variables according to the control signal while satisfying all constraints. A proportional–integral–derivative controller is shown to be computationally efficient. Numerical issues involving local minima, mesh dependency, checkerboard patterns, and intermediate densities are tackled using continuation, filtering, and penalization methods. The performance of this algorithm is demonstrated for unpenalized and penalized topology optimization problems.

An earlier study introduced the concept of piezoelectric energy-harvesting skin (EHS) to harvest energy by attaching thin piezoelectric patches onto a vibrating skin. This paper presents a methodology for the optimum design of EHS with the use of an efficient topology optimization method referred to as the hybrid cellular automaton (HCA) algorithm. The design domain of the piezoelectric material is discretized into cellular automata (CA), and the response of each CA is measured using high-fidelity finite-element analysis of a vibrating structure. The CA properties are parameterized using nonlinear interpolation functions that follow the principles of the SIMP model. The HCA algorithm finds the optimal densities and polarizing directions at each CA that maximize the output power from the EHS. The performance of this approach is demonstrated for the optimal design of EHS in two real-world case studies.

Design for structural topology optimization is a method of distributing material within a design domain of prescribed dimensions. This domain is discretized into a large number of elements in which the optimization algorithm removes, adds, or maintains the amount of material. The resulting structure maximizes a prescribed mechanical performance while satisfying functional and geometric constraints. Among different topology optimization algorithms, the hybrid cellular automaton (HCA) method has proven to be efficient and robust in problems involving large, plastic deformations. The HCA method has been used to design energy absorbing structures subject to crash impact. The goal of this investigation is to extend the use of the HCA algorithm to the design of an advanced composite armor (ACA) system subject to a blast load. The ACA model utilized consists of two phases: ceramic and metallic. In this work, the proposed algorithm drives the optimal distribution of a metallic phase within the design domain. When the blast pressure wave hits the targeted structure, the fluids kinetic energy is transformed into strain energy (SE) inside the solid medium. Maximum attenuation is reached when SE is maximized. Along with an optimum use of material, this condition is satisfied when SE is uniformly distributed in the design domain. This work makes use of the CONWEP model developed by the Army Research Laboratory. The resulting structure shows the potential of the HCA method when designing ACAs.

An objective in crashworthiness design is to obtain energy-absorbing components. This task has been efficiently undertaken using the Hybrid Cellular Automaton method. This method combines the CA paradigm with nonlinear, dynamic finite element analysis. Lightweight, energy-absorbing topology concepts have been obtained with this approach. This paper furthers the development of the HCA method to an efficient tool for synthesising shell structures using topometry optimisation. The objective is to find the thickness distribution that uniformly distributes the structures internal energy density. This approach addresses problems involving collisions, large displacement and material plastic hardening. The final designs meet manufacturing and performance constraints.

This research introduces a multidomain topology optimization algorithm for crashworthy structure undergoing large deformations. This technique makes use of the hybrid cellular automaton framework, which combines transient, non-linear finite-element analysis and local control rules acting on cells. The set of all cells defines the multidomains. Each subdomain has been defined by different material update rules according to specify constraint, and optimization iteration of each subdomain has been converged respectively during the optimal design process. The effectiveness of this technique is demonstrated through the design of a bumper-like structure. Result show that the new algorithm is suitable for practical applications. The case study presented demonstrates the potential significance of this work for a wide range of engineering design problems.

The hybrid cellular automaton (HCA) method is a biologically inspired algorithm capable of topology synthesis that was developed to simulate the behavior of the bone functional adaptation process. In this algorithm, the design domain is divided into cells with some communication property among neighbors. Local evolutionary rules, obtained from classical control theory, iteratively establish the value of the design variables in order to minimize the local error between a field variable and a corresponding target value. Karush-Kuhn-Tucker (KKT) optimality conditions have been derived to determine the expression for the field variable and its target. While averaging techniques mimicking intercellular communication have been used to mitigate numerical instabilities such as checkerboard patterns and mesh dependency, some questions have been raised whether KKT conditions are fully satisfied in the final topologies. Furthermore, the averaging procedure might result in cancellation or attenuation of the error between the field variable and its target. Several examples are presented showing that HCA converges to different final designs for different neighborhood configurations or averaging schemes. Although it has been claimed that these final designs are optimal, this might not be true in a precise mathematical sense—the use of the averaging procedure induces a mathematical incorrectness that has to be addressed. In this work, a new adaptive neighboring scheme will be employed that utilizes a weighting function for the influence of a cell’s neighbors that decreases to zero over time. When the weighting function reaches zero, the algorithm satisfies the aforementioned optimality criterion. Thus, the HCA algorithm will retain the benefits that result from utilizing neighborhood information, as well as obtain an optimal solution.

Structural design for crashworthiness is a challenging area of research due to large plastic deformations and complex interactions among diverse components of the vehicle. Previous research in this field primarily focused on energy absorbing structures that utilise a desired amount of material. These structures have been shown to absorb a large amount of the kinetic energy generated during the crash event; however, the large plastic strains experienced can lead to material failure and loss of structural integrity. This research introduces a strain-based, dynamical multi-domain topology optimisation algorithm for crashworthy structures undergoing large deformations. This technique makes use of the hybrid cellular automaton framework, which combines transient, non-linear finite-element analysis and local control rules acting on cells. The set of all cells defines the design domain. In the proposed algorithm, the design domain is dynamically divided into two sub-domains for different objectives, i.e., high-strain sub-domain (HSSD) and low-strain sub-domain (LSSD). The distribution of these sub-domains is determined by a plastic strain limit value. During the design process, the material is distributed within the LSSD to distribute internal energy uniformly. In the HSSD, the material is distributed to satisfy a failure criterion given by a maximum strain value. Results show that the new formulation and algorithm are suitable for practical applications. The case study presented demonstrates the potential significance of this work for a wide range of engineering design problems.

The primary objective of this investigation is the optimum design of lightweight foam material systems for controlled energy absorption under blast impact. The ultimate goal of these systems is to increase the safety and integrity of occupants and critical components in structural systems such as automotive vehicles, buildings, ships, and aircrafts. Although outstanding results have been achieved with the use of foams in blast protective systems, current design practices rely on trial and error as there is an absence of a systematic design method. While the governing equations are known for a variety of physical phenomena in appropriate length scales, there are no suitable methodologies to accomplish the aforementioned objectives. A promising approach to systematically design the material's microstructure is the use of structural optimization methods. This investigation presents an appropriate design methodology to optimally design foam material systems for blast mitigation. The objective function is expressed in terms of acceleration. Macroscopic effective material properties are used to drive the nonlinear analysis of the elasto-plastic material under time-dependent loading conditions. Gradient-based optimization methods are used to obtain the final density distribution of the foam material system. The application of this approach is shown through a two-dimensional optimization problem.

The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is affected by parameters of the algorithm. As a result, questions have been raised regarding the conditions by which HCA converges to an optimal design. The objective of this investigation is to examine the conditions that guarantee convergence to a Karush-Kuhn-Tucker (KKT) point. In this paper, it is shown that the HCA algorithm is a fixed point iterative scheme and the previously reported KKT optimality conditions are corrected. To demonstrate the convergence properties of the HCA algorithm, a simple cantilevered beam example is utilized. Plots of the spectral radius for projections of the design space are used to show regions of guaranteed convergence.