Optimal Stiffness Research Articles

Fiber orientation and boundary stiffness optimization of laminated cylindrical shells with elastic boundary for maximum the fundamental frequency by an improved sparrow search algorithm

In this paper, a multivariate improved sparrow search algorithm (MCSSA) is proposed for maximizing the fundamental frequency of composite laminated cylindrical shells and preventing vibrational resonance. The mathematical model for analyzing the fundamental frequency of composite laminated cylindrical shells in free vibration is established based on the first-order shear deformation theory (FSDT). A fundamental frequency optimization model for composite laminated cylindrical shells with elastic boundary is formulated, considering the influence of fiber orientation and boundary stiffness, with the objective of maximizing the fundamental frequency. In the optimization process, in response to the shortcomings of the sparrow search algorithm, Piecewise Linear Chaotic Map (PWLCM), tracking learning strategy, opposition-based learning strategy (OBL) and elite retention strategy are introduced for improvement to obtain the MCSSA with better overall performance for model optimization. The effectiveness and applicability of the algorithm improvements are demonstrated by comparing MCSSA with the whale optimization algorithm (WOA), sparrow search algorithm (SSA), and pelican optimization algorithm (POA) using 13 standard test functions and 2 composite laminated cylindrical shell cases. The numerical calculation results show that the shells optimized with MCSSA have higher fundamental frequency. MCSSA is an effective candidate for solving such problems.

Fatigue life improvement mechanisms of CFRP/Al hybrid joints – Load sharing study using a digital image correlation technique

In comparison with an adhesive joint, a hybrid joint often provides a more effective and reliable way to meet heightened safety requirements in engineering like FAA AC 20-107B. Nevertheless, its fatigue failure characterization, life improvement mechanism and engineering design approach have been understudied as compared to the static loading condition. This study aims to characterize the failure mechanisms by use of the digital image correlation (DIC) technique for elucidating the load sharing phenomenon of hybrid joints in the course of fatigue failure. In the study, bonded, riveted and hybrid joints were tested under static and fatigue loading conditions. To explore different mechanical behaviors of hybrid joints, two types of adhesives with an evident difference in modulus were selected to fabricate the joints. The fatigue life of an adhesive layer and that of the hybrid joint were investigated respectively to explore the means for life improvement. It is shown that the fatigue life of the hybrid joint can be significantly improved as a result of load sharing by rivets. The improvement of the fatigue life could reach 5 to 13 folders for the hybrid joint due to the load sharing, whereas its improvement ratio was only 1–2 times when the adhesive and the rivet were used independently. By considering the overlap area as an effective region for design of rivet group, an optimal stiffness can be obtained for the hybrid joint. This study identifies two completely different fatigue failure processes for hybrid joints and illustrates the improvement mechanisms of fatigue life, thereby providing a useful guidance for optimal design of hybrid joints.

Kinetostatics-based stiffness analysis of continuum manipulators considering non-constant cross sections

Continuum manipulators are widely used for their compliant and dexterous nature, but their design and modeling are simplified by keeping the cross-section constant. Inspired by biological structures like elephant trunks and octopus tentacles, previous studies have proposed continuum manipulators featuring non-constant cross sections, but few of them study how the cross sections affect the manipulator’s properties, such as stiffness. In this paper, a general kinetostatic model and a stiffness model are presented for continuum manipulators with non-constant cross sections and experimental validations are conducted under various actuating and loading conditions. Moreover, comparative stiffness analysis is performed among manipulator designs with different non-constant cross sections. The results indicate a significant impact of cross-section-varying rates on the system stiffness along different directions. This approach and analysis are significant for the structure design and stiffness optimization of continuum manipulators, particularly in applications where stiffness is a primary objective.

Force-dependent focal adhesion assembly and disassembly: A computational study.

Cells interact with the extracellular matrix (ECM) via cell-ECM adhesions. These physical interactions are transduced into biochemical signals inside the cell which influence cell behaviour. Although cell-ECM interactions have been studied extensively, it is not completely understood how immature (nascent) adhesions develop into mature (focal) adhesions and how mechanical forces influence this process. Given the small size, dynamic nature and short lifetimes of nascent adhesions, studying them using conventional microscopic and experimental techniques is challenging. Computational modelling provides a valuable resource for simulating and exploring various "what if?" scenarios in silico and identifying key molecular components and mechanisms for further investigation. Here, we present a simplified mechano-chemical model based on ordinary differential equations with three major proteins involved in adhesions: integrins, talin and vinculin. Additionally, we incorporate a hypothetical signal molecule that influences adhesion (dis)assembly rates. We find that assembly and disassembly rates need to vary dynamically to limit maturation of nascent adhesions. The model predicts biphasic variation of actin retrograde velocity and maturation fraction with substrate stiffness, with maturation fractions between 18-35%, optimal stiffness of ∼1 pN/nm, and a mechanosensitive range of 1-100 pN/nm, all corresponding to key experimental findings. Sensitivity analyses show robustness of outcomes to small changes in parameter values, allowing model tuning to reflect specific cell types and signaling cascades. The model proposes that signal-dependent disassembly rate variations play an underappreciated role in maturation fraction regulation, which should be investigated further. We also provide predictions on the changes in traction force generation under increased/decreased vinculin concentrations, complementing previous vinculin overexpression/knockout experiments in different cell types. In summary, this work proposes a model framework to robustly simulate the mechanochemical processes underlying adhesion maturation and maintenance, thereby enhancing our fundamental knowledge of cell-ECM interactions.

CF Reinforced Thermoplastic Hybrid Process Proposal for the Optimization of Sandwich Panels Stiffness and Processability

The development of composite materials has meant, over the last few decades, a challenge for research in relation to the search for new ways of manufacturing. Currently, a wide variety of materials and processes have a high degree of development and industrial applications, but the potential for improvement in this area promotes the search for new systems that allow obtaining products with better mechanical characteristics and better manufacturability. Within this framework of the development of processes and applications, the following combination of manufacturing technologies is proposed: thermoforming and overmolding of carbon fiber reinforced thermoplastics with continuous and short fibers respectively. The aim of this work is to provide a hybrid technology to manufacture sandwich panels whose stiffening core geometry can be highly optimized based on the load requirements considered in the design of the product of interest. The proposed process consists of the prior shaping by thermoforming process of a continuous fiber-reinforced thermoplastic laminate on one of the surfaces of the manufacturing mold that will later be used for injection of the core structure with a counter-mold adapted for this purpose. The injection of the short fiber reinforced thermoplastic will be carried out in such a way that one of the surfaces of the resulting cavity is directly in contact with the previously formed laminate, giving rise to an overmolding. After this operation, a closing laminate will be formed that will give the panel the desired resistance. A detailed analysis of the different stages of this process is necessary, especially with regard to the processing parameters (e.g. injection temperature, pressure, polymer velocity, and interface temperature), orientation of the fiber resulting from the injection process, the adhesion of the polymer between stages, and the geometric limitations of considered sub-processes. The analysis is performed using a finite element method (FEM) software and analytical approaches.

Aero-structural coupled optimization of a rotor blade for an upscaled 25 MW reference wind turbine

One major challenge of the wind turbine industry is the reduction of the levelized cost of energy (LCoE) while following the strong demand for a higher annual energy production (AEP). To meet these goals, larger wind turbine sizes are required. The common method of upscaling existing wind turbine designs comes along with the problem of faster growing blade masses and costs compared to the AEP. Investigations in new technologies to improve the structural efficiency of larger blades can be supported by aero-structural coupled optimizations. The present work introduces a two-step aero-structural coupled design process to capture the multi-disciplinary trade-offs between costs and AEP, aiming at minimizing LCoE for a 25 MW wind turbine. In a first step, a preliminary aero-structural optimisation is carried out using simplified and fast methods. The output is then refined with respect to additional design criteria with an advanced optimization process, including an aero-servo-elastic coupled loads analysis. The process is applied to a 25 MW blade, upscaled from the IEA 15 MW reference wind tubine. Based on the results of an utilization analysis, the structural design is adapted, and a stiffness optimization is performed. The optimum airfoil positions are identified to reduce the amount of material while limiting losses in the aerodynamic performance. The obtained blade designs facilitate a consistent AEP compared to the upscaled reference design. A mass reduction of 35% could be achieved, which results in a reduced LCoE of 1.7% compared to the purely upscaled blade design.

Determination of the Orthotropic Mechanical Elastic Properties of Gas Diffusion Layers for PEMFCs

One of the most important components of proton exchange membrane fuel cell is the gas diffusion layer (GDL), due to its position between the catalyst layers, where the electrochemical reactions take place, and the bipolar plates supplying the reactant gases. The GDL must have an optimal mechanical stiffness to ensure the transport of the different gases and the water produced by the fuel cell operation. Measuring the mechanical properties of the different GDLs available in the market require the development of specific methodologies due to their orthotropic behavior. This article aims to assess and create a database for selecting GDLs for specific applications and assisting engineers in fuel cell modeling. This study focuses on developing robust characterization methods to assess the different properties of GDLs in different directions: within the plane, along both the machine and transverse directions, and perpendicular to the plane. These tests allow to determine parameters like in-plane tensile and shear moduli, out-of-plane compression and shear moduli, and in-plane Poisson’s ratios. By examining a wide range of commercial specimens, including different types, area weights, hydrophobic treatments, manufacturing processes, and microporous layers, this study aims to provide a comprehensive analysis of the orthotropic mechanical properties of GDLs.

Optimization of machining performance in deep hole boring: A study on cutting tool vibration and dynamic vibration absorber design

In the realm of precision engineering, particularly in deep hole boring processes, tool vibration emerges as a critical determinant of machining performance. This investigation elucidates the genesis of self-excited vibrations within deep hole boring operations and delineates the underlying mechanisms of cutting tool vibration. A focal point of this study is the optimal alignment of the boring bar to mitigate vibrational impacts, thereby enhancing surface finish quality and extending tool longevity. Central to this analysis is the employment of a Dynamic Vibration Absorber (DVA) aimed at attenuating cutting tool vibration. The deployment of DVA necessitates precise identification of modal parameters, namely the equivalent stiffness (K) and mass (M) of the cutting tool. This research juxtaposes various scholarly methodologies to amalgamate theoretical calculations with simulation approaches, thereby acquiring accurate modal parameters. Utilizing Matlab software, the vibration amplitude of the boring bar under varying spring stiffness scenarios was examined. Results indicate a direct correlation between increased stiffness and reduced amplitude, particularly when the frequency ratio 'g' ranges between 0.5 and 1.1. Consequently, a stiffer DVA configuration is posited as more effective in vibration reduction. Furthermore, the study conducted frequency sweep experiments on a damping boring bar, utilizing a vibration excitation platform. These experiments revealed the existence of an optimal stiffness value for the DVA, thereby underscoring the significance of stiffness matching in vibration mitigation strategies.

A Comparative Analysis of the Response-Tracking Techniques in Aerospace Dynamic Systems Using Modal Participation Factors

Mechanical structural systems are subject to multiple dynamic disturbances during service. While several possible scenarios can be examined to determine their design loading conditions, only a relatively small set of such scenarios is considered critical. Therefore, only such particular deterministic set of critical load cases is commonly employed for the structural design and optimization. Nevertheless, during the design and optimization stages, the mass and stiffness distributions of such assemblies vary, and, in consequence, their dynamic response also varies. Thus, it is important to consider the variations in the dynamic loading conditions during the design-and-optimization cycles. This paper studies the modal participation factors at length and proposes an alternative to the current point-wise treatment of the dynamic equations of motion of flexible bodies during design optimization. First, the most relevant-to-structural-dynamics definitions available in the literature are reviewed in depth. Second, the analysis of those definitions that have the potential to be adopted as point-wise constraint equations during structural optimization is extended. Finally, a proof of concept is presented to demonstrate the usability of each definition, followed by a case study in which the potential advantages of the proposed extended analysis are shown.

Simultaneous optimization of stiffness, permeability, and surface area in metallic bone scaffolds

Metallic bone scaffolds fabricated by selective laser melting (SLM) have attracted significant attention in bone tissue engineering. Scaffolds based on triply periodic minimal surfaces (TPMS) are currently the subject of extensive investigation, making them a fitting benchmark for evaluating novel architectures. In this study, we introduced and assessed the viability of modified face-centered cubic (MFCC) scaffolds as an alternative to TPMS scaffolds. Two distinct categories of TPMS scaffolds, namely sheet TPMS and skeletal TPMS, were examined for comparative analysis. Employing finite element method (FEM) and computational fluid dynamics (CFD) analysis, we comprehensively evaluate the MFCC and TPMS scaffolds from structure, fluid flow, surface area, and surface curvature perspectives. Among the investigated porosities (75%, 80% and 85%), the MFCC scaffold category consistently exhibited dominant designs on the Pareto front, whereas the majority of TPMS scaffolds failed to achieve multiobjective optimality. MFCC scaffolds exhibited superior mechanical properties compared to skeletal TPMS scaffolds, while also demonstrating improved fluid flow characteristics in contrast to sheet TPMS scaffolds. Furthermore, MFCC scaffolds possessed a specific surface area that fell within the range observed in natural bone tissue, thereby bridging a crucial gap in the design space for optimizing bone scaffolds. The concave internal surfaces of MFCC scaffolds showed promising potential for enhancing bone cell growth. Selective laser melting (SLM) was employed to fabricate the designed scaffolds using stainless steel 316L. Subsequently, uniaxial compression tests were conducted on these scaffolds to validate the accuracy of the simulation results. This study provides valuable insights into multiobjective design and optimization of bone scaffolds, highlighting the significance of MFCC scaffolds as a valuable addition to the existing library of bone scaffold architectures.

Stiffness on shear wave elastography as a potential microenvironment biomarker for predicting tumor recurrence in HBV-related hepatocellular carcinoma

BackgroundTo explore the pathologic basis and prognostic value of tumor and liver stiffness measured pre-operatively by two-dimensional shear wave elastography (2D-SWE) in hepatitis B virus (HBV)-related hepatocellular carcinoma (HCC) patients who undergo hepatic resection.MethodsA total of 191 HBV-infected patients with solitary resectable HCC were prospectively enrolled. The stiffness of intratumoral tissue, peritumoral tissue, adjacent liver tissue, and distant liver tissue was evaluated by 2D-SWE. The correlations between stiffness and pathological characteristics were analyzed in 114 patients. The predictive value of stiffness for recurrence-free survival (RFS) was evaluated, and Cutoff Finder was used for determining optimal cut-off stiffness values. Cox proportional hazards analysis was used to identify independent predictors of RFS.ResultsPathologically, intratumoral stiffness was associated with stroma proportion and microvascular invasion (MVI) while peritumoral stiffness was associated with tumor size, capsule, and MVI. Adjacent liver stiffness was correlated with capsule and liver fibrosis stage while distant liver stiffness was correlated with liver fibrosis stage. Peritumoral stiffness, adjacent liver stiffness, and distant liver stiffness were all correlated to RFS (all p < 0.05). Higher peritumoral stiffness (> 49.4 kPa) (HR = 1.822, p = 0.023) and higher adjacent liver stiffness (> 24.1 kPa) (HR = 1.792, p = 0.048) were significant independent predictors of worse RFS, along with tumor size and MVI. The nomogram based on these variables showed a C-index of 0.77 for RFS prediction.ConclusionsStiffness measured by 2D-SWE could be a tumor microenvironment and tumor invasiveness biomarker. Peritumoral stiffness and adjacent liver stiffness showed important values in predicting tumor recurrence after curative resection in HBV-related HCC.Clinical relevance statementTumor and liver stiffness measured by two-dimensional shear wave elastography serve as imaging biomarkers for predicting hepatocellular carcinoma recurrence, reflecting biological behavior and tumor microenvironment.Key points• Stiffness measured by two-dimensional shear wave elastography is a useful biomarker of tumor microenvironment and invasiveness.• Higher stiffness indicated more aggressive behavior of hepatocellular carcinoma.• The study showed the prognostic value of peritumoral stiffness and adjacent liver stiffness for recurrence-free survival.• The nomogram integrating peritumoral stiffness, adjacent liver stiffness, tumor size, and microvascular invasion showed a C-index of 0.77.Graphical

Buckling analysis and optimization of variable angle tow composite plates via Ritz method and variable stiffness optimization

A novel variable stiffness optimization (VSO) algorithm is proposed accounting for the inherent mechanical characteristics of variable angle tow (VAT) plates. Through sampling in the design space of lamination parameters (LPs), a good initial point is identified in stacking sequence design domain. The concept of tailoring stiffness point by point through-thickness is then introduced. By using the linear fiber path function, design variables for VAT plates are divided into three groups, and then a layerwise optimization approach (LOA) is applied to optimize the angles from the outermost to the innermost stacking position within the three groups, sequentially and iteratively. Through a point-by-point optimization of fiber paths, the stiffness of VAT plates is enhanced part by part. Ritz-type buckling solutions are presented for VAT composite plates with arbitrary boundary conditions. Using first-order shear deformation theory (FSDT), the translational and rotational degrees of freedom of the plate are divided into in-plane and out-of-plane components to solve the prebuckling and buckling problems independently. Buckling loads of VAT plates are optimized under multiple boundary conditions and loadings. Results indicate that VSO algorithm is efficient and robust, and the buckling resistance capacity of optimized VAT plates can be improved approximately twice over constant-stiffness laminates.

The interaction between muscle pathophysiology, body mass, walking speed and ankle foot orthosis stiffness on walking energy cost: a predictive simulation study

BackgroundThe stiffness of a dorsal leaf AFO that minimizes walking energy cost in people with plantarflexor weakness varies between individuals. Using predictive simulations, we studied the effects of plantarflexor weakness, passive plantarflexor stiffness, body mass, and walking speed on the optimal AFO stiffness for energy cost reduction.MethodsWe employed a planar, nine degrees-of-freedom musculoskeletal model, in which for validation maximal strength of the plantar flexors was reduced by 80%. Walking simulations, driven by minimizing a comprehensive cost function of which energy cost was the main contributor, were generated using a reflex-based controller. Simulations of walking without and with an AFO with stiffnesses between 0.9 and 8.7 Nm/degree were generated. After validation against experimental data of 11 people with plantarflexor weakness using the Root-mean-square error (RMSE), we systematically changed plantarflexor weakness (range 40–90% weakness), passive plantarflexor stiffness (range: 20–200% of normal), body mass (+ 30%) and walking speed (range: 0.8–1.2 m/s) in our baseline model to evaluate their effect on the optimal AFO stiffness for energy cost minimization.ResultsOur simulations had a RMSE < 2 for all lower limb joint kinetics and kinematics except the knee and hip power for walking without AFO. When systematically varying model parameters, more severe plantarflexor weakness, lower passive plantarflexor stiffness, higher body mass and walking speed increased the optimal AFO stiffness for energy cost minimization, with the largest effects for severity of plantarflexor weakness.ConclusionsOur forward simulations demonstrate that in individuals with bilateral plantarflexor the necessary AFO stiffness for walking energy cost minimization is largely affected by severity of plantarflexor weakness, while variation in walking speed, passive muscle stiffness and body mass influence the optimal stiffness to a lesser extent. That gait deviations without AFO are overestimated may have exaggerated the required support of the AFO to minimize walking energy cost. Future research should focus on improving predictive simulations in order to implement personalized predictions in usual care.Trial Registration Nederlands Trial Register 5170. Registration date: May 7th 2015. http://www.trialregister.nl/trialreg/admin/rctview.asp?TC=5170

A Dual-Inlet Pump with a Simple Valves System.

To ameliorate the deficient output flow performance of the piezoelectric pumps with cantilever valves, a dual-inlet pump with a simple valves system is proposed. On the basis of explaining the structure design of the prototype, the working principle of the prototype is explained, and the output flow is theoretically analyzed. Then, the manufacturing process of the prototype is introduced. The general operating frequency of the pump was obtained by combining the finite element analysis of the piezoelectric actuator under dry and wet modes with the mechanical vibration test, and a series of measured flow rates were compared and improved through valve stiffness optimization and pump chamber height adjustment in the subsequent control experiment. The proposed piezoelectric pump achieves a maximum flow rate of 33.18 mL/min at a 180 Vp-p voltage with the driving frequency of 100 Hz, which may bring new inspiration for the application of small intelligent pumps in the field of microfluidics.

Bio-Inspired Aquatic Propulsion Mechanism Using Viscoelastic Fin Containing Fiber Composite Shear Thickening Fluid.

Many propulsion mechanisms utilizing elastic fins inspired by the caudal fins of aquatic animals have been developed. However, these elastic fins possess a characteristic whereby the rigidity required to achieve propulsion force and speed increases as the oscillation velocity increases. Therefore, by adding an actuator including a variable stiffness mechanism to the fin it is possible to maintain the optimal stiffness at all times. However, if the aforementioned characteristics allowing the fin itself to change stiffness are present, the need for a variable stiffness mechanism is eliminated, leading to possibilities such as the simplification of the mechanism, improvements in fault tolerance, and enhancements in fin efficiency. The authors developed a fiber composite viscoelastic fin by adding fibers to a shear thickening fluid (STF) and examined the speed dependency of the fin's rigidity. In this work, we examined the structure and speed dependency of the fin's rigidity, as well as the propulsion characteristics in still water and in uniform flow. As a result, the fiber-containing fin containing the STF oobleck (an aqueous suspension of potato starch) demonstrated higher propulsion in still water and higher self-propelled equivalent speed in uniform water flow than elastic fins.

Damping characteristics and sound transmission loss of finite composite plates with frequency dependent constrained viscoelastic interlayer

This paper proposes a sublaminate layer-wise finite element modeling method to accurately evaluate the damping and sound insulation characteristics of composite constrained layer damping plates. It incorporates the frequency-dependent property of viscoelastic interlayer into fully coupled structure-acoustic interaction equations, and employs the generalized high-order displacement hypothesis with tailored polynomial series expansion. The method is applicable to various boundary conditions and material layer combinations. Validation is conducted using numerical and experimental data. Parametric study identifies optimal thickness and stiffness for maximizing modal loss factor. Additionally, sound insulation performance is examined in narrow frequency bands, highlighting the damping enhancement of viscoelastic interlayer.

Hydraulic variable stiffness mechanism for swimming locomotion optimization of soft robotic fish

In this paper, we describe the development of a soft robotic fish with Hydraulic Variable Stiffness (HVS), a simple and light mechanism that actively controls the tail stiffness. Modal analysis model using PRBM was developed to predict the tendency of optimal tail stiffness which maximizes the forward swimming speed in response to driving frequency. The forward swimming locomotion experiment demonstrated that the optimal tail stiffness which maximizes swimming speed exists for each driving frequency, and that optimal stiffness increases as the frequency increases. The turning locomotion experiment showed that, as the tail stiffness decreases, the turning radius decreases and the turning angular velocity increases significantly. By controlling the tail stiffness to its optimal for specific locomotion, the robot can increase its swimming speed by 118% on average, reduce its turning radius to almost a quarter, and increase its turning angular velocity by almost three times. These results demonstrate that the HVS soft robotic fish can optimize its swimming locomotion more effectively compared to conventional robots by optimizing its tail stiffness depending on its required swimming situation with only one actuator to oscillate the tail using the HVS device.

Seismic performance of buffer-equipped anchored piles considering end restraints

During seismic events, slopes buttressed by anchored piles can experience instability when piles convert to perilous cantilever systems upon anchor cables failure. Implementing buffer devices in anchoring structures has the potential to reduce the seismic forces in the anchors and consequently improve the seismic performance of the supported structures. Taking advantage of the excellent ductility of flexible piles, this study investigates a buffer device installed in series with the anchored piles. Shaking table tests were conducted on a slope stabilized by buffer-equipped anchored piles considering two typical pile tip conditions: either hinged or free end restraints. Three ground motions with different characteristics were applied to the model slopes fitted with springs with varying stiffness and its seismic response was evaluated in terms of soil accelerations, pile displacements, earth pressures, and anchor-cable forces. In addition, the cable loading reduction mechanism was investigated through the force Fourier spectrum. The results indicated that the system dominant frequency decreased for anchor with hinge support and the pile displacement increased and the dynamic earth pressure decreased as the spring stiffness decreased. Most importantly, implementing the buffer device (i.e., the spring) reduced the response energy significantly over the whole frequency range, especially in the middle range, which resulted in a marked reduction in the anchor cable stress and fatigue damage. The reduction of anchor force was found to be inversely correlated with the spring stiffness. Based on the maximum pile displacement and spring stroke, a stiffness optimization strategy was proposed considering the foundation conditions and seismic excitations. For major earthquakes, stiff springs are advisable to mitigate load effects and to help maintain pile displacement within permissible bounds, while the spring stiffness can be reduced appropriately by implementing a hinge support. Meanwhile, the design should focus on critical displacement rather than loading reduction for seismic hazard characterized by near field earthquakes or high peak ground acceleration.

Multimaterial Topology Optimization of Adhesive Backing Layers via J-Integral and Strain Energy Minimizations

Abstract Strong adhesives often rely on reduced stress concentrations obtained via specific functional grading of material properties. This can be seen in many examples in nature and engineering. Basic design principles have been formulated based on parametric optimization, but a general design tool is still missing. We propose here the use of topology optimization to achieve optimal stiffness distribution in a multimaterial adhesive backing layer, reducing stress concentration at selected (crack tip) locations. The method involves the minimization of a linear combination of (i) the J-integral around the crack tip and (ii) the strain energy of the structure. This combination is due to the compromise between numerical stability and accuracy of the method, where (i) alone is numerically unstable and (ii) alone cannot eliminate the crack tip stress singularity. We analyze three cases in plane strain conditions, namely, (1) double-edged crack and (2) center crack, in tension, as well as (3) edge crack under shear. Each case evidences a different optimal topology with (1) and (2) providing similar results. The optimal topology allocates stiffness in regions that are far away from the crack tip, and the allocation of softer materials over stiffer ones produces a sophisticated structural hierarchy. To test our solutions, we plot the contact stress distribution across the interface. In all observed cases, we eliminate the stress singularity at the crack tip, albeit generating (mild) stress concentrations in other locations. The optimal topologies are tested to be independent of the crack size. Our method ultimately provides the robust design of flaw tolerant adhesives where the crack location is known.

Minimizing Energy Consumption of Elastic Robots in Repetitive Tasks

Energy consumption is an important issue in robotics. This article deals with the problem of reducing the energy consumption of compliant electro-mechanical systems while performing periodic tasks. After deriving performance indices to quantify the energy consumption of a mechanical system, we propose a method to determine both the optimal compliant actuation parameters, and link trajectories to minimize energy consumption. We show how this problem can be cast in a simpler one where the optimization regards only parameters that define the shape of periodic trajectories to be subsequently determined by using numerical optimization tools. Indeed, in our framework, the optimal stiffness and spring preload can be analytically obtained as a function of the desired link trajectories. We then provide simulations and experimental validations of the obtained results on a two-link compliant manipulator platform which performs a repetitive pick-and-place task. Our experiments show that the use of compliant actuators instead of rigid ones and the optimization of their compliant parameters give rise to an energy saving up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$62\%$</tex-math> </inline-formula> with respect to rigid actuation. Moreover, the simultaneous optimization of the compliant parameters and link trajectories provide an additional energy saving up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$20\%$</tex-math> </inline-formula> .