Stiffness Distribution Research Articles

Kirigami-based inverse design for 3D surfaces formed by mechanically guided method

The mechanically guided assembly method utilizes the compressive buckling behavior of thin-film structures to transform two-dimensional (2D) precursors into three-dimensional (3D) structures. Previous research has shown that by inverse designing thickness and width distributions in 2D precursors, various 3D surfaces with target geometries can be accurately assembled. However, the variation in thickness poses significant challenges for the fabrication of the 2D precursor, especially on a small scale. In this paper, we propose a Kirigami-based inverse design framework that utilizes pre-specified incision patterns as critical parameters to control the bending stiffness distribution of 2D precursors. This enables the fabrication of target 3D structures with constant thickness, which greatly simplifies the production of 2D precursors. By studying the deformation characteristics of beam models during pure bending, we have established an analytical relationship between incision patterns and bending stiffness distribution. To validate the effectiveness of our inverse design theory, we conducted a series of simulations and experiments on 3D structures, yielding favorable comparison results. Moreover, guided by this inverse design theory, we have developed a microneedle structure through conceptual design, demonstrating the capability of Kirigami patterns in the inverse design of complex 3D structures, and highlighting the potential application of our method in the biomedical field.

A Comparative Analysis of Optimization Algorithms for Finite Element Model Updating on Numerical and Experimental Benchmarks

Finite Element Model Updating (FEMU) is a common approach to model-based Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM) of civil structures and infrastructures. Its application can be further utilized to produce effective digital twins of a permanently monitored structure. The FEMU concept, simple yet effective, involves calibrating and/or updating a numerical model based on the recorded dynamic response of the target system. This enables to indirectly estimate its material parameters, thus providing insight into its mass and stiffness distribution. In turn, this can be used to localize structural changes that may be induced by damage occurrence. However, several algorithms exist in the scientific literature for FEMU purposes. This study benchmarks three well-established global optimization techniques—namely, Generalized Pattern Search, Simulated Annealing, and a Genetic Algorithm application—against a proposed Bayesian sampling optimization algorithm. Although Bayesian optimization is a powerful yet efficient global optimization technique, especially suitable for expensive functions, it is seldom applied to model updating problems. The comparison is performed on numerical and experimental datasets based on one metallic truss structure built in the facilities of Cranfield University. The Bayesian sampling procedure showed high computational accuracy and efficiency, with a runtime of approximately half that of the alternative optimization strategies.

Influence of rebar couplers on the cracking behavior of reinforced concrete beams

Mechanical connections of rebars are widely used and demonstrated high effectiveness in reinforced concrete structural elements, but the differences in the performances of different connection methods in reinforced concrete beams from the perspective of adhesion, bending, and load transfer are rarely documented. In addition, existing rebar connections are large and may lead to local cracking because of their size. In this study, we investigated the use of compact mechanical couplers by pull-out tests and bending tests of full-scale reinforced concrete beams. For pull-out tests, the influence of the couplers position in concrete was studied. Different rebar configurations were tested for beams: continuous, with a covering, or connected with compact mechanical couplers. The nonlinear behaviour of beams was analysed under monotonic and cyclic load conditions. The overall behaviour of beams is discussed in terms of load–displacement curves and concrete cracking distribution. To study the local behaviour, digital image correlation was set up, allowing to monitor strain distribution and crack opening.Experimental results show no significant impact of the compact couplers on the global or local behaviour of reinforced concrete beams compared to the beams using continuous rebars: failure load, overall stiffness, and crack distribution are similar, in the uncertainty range of tests. The regulatory calculation of crack openings and spacing fits the experimental results for most of the studied cases.

Path Planning and Bending Behaviors of 3D Printed Continuous Carbon Fiber Reinforced Polymer Honeycomb Structures.

Continuous fiber reinforced polymer composites are widely used in load-bearing components and energy absorbers owing to their high specific strength and high specific modulus. The path planning of continuous fiber is closely related to its structural defects and mechanical properties. In this work, continuous fiber reinforced polymer honeycomb structures (CFRPHSs) with different printing paths were designed and fabricated via the fused deposition modeling (FDM) technique. The investigation of fiber dislocation at path corners was utilized to analyze the structural defects of nodes caused by printing paths. The lower stiffness nodes filled with pure polymer due to fiber dislocation result in uneven stiffness distribution. The bending performance and deformation modes of CFRPHSs with different printing paths and corresponding pure polymer honeycomb structures were investigated by three-point bending tests. The results showed that the enhancement effect of continuous fibers on the bending performance of honeycomb structures was significantly affected by the printing paths. The CFRPHSs with a staggered trapezoidal path exhibited the highest specific load capacity (68.33 ± 2.25 N/g) and flexural stiffness (627.70 ± 38.78 N/mm). In addition, the fiber distributions and structural defects caused by the printing paths determine the stiffness distribution of the loading region, thereby affecting the stress distribution and failure modes of CFRPHSs.

System reliability-based robust design of deep foundation pit considering multiple failure modes

Recently, reliability-based design is a universal method to quantify negative influence of uncertainty in geotechnical engineering. However, for deep foundation pit, evaluating the system safety of retaining structures and finding cost-effective design points are main challenges. To address this, this study proposes a novel system reliability-based robust design method for retaining system of deep foundation pit and illustrated this method via a simplified case history in Suzhou, China. The proposed method included two parts: system reliability model and robust design method. Back Propagation Neural Network (BPNN) is used to fit limit state functions and conduct efficient reliability analysis. The common source random variable (CSRV) model are used to evaluate correlation between failure modes and determine the system reliability. Furthermore, based on the system reliability model, a robust design method is developed. This method aims to find cost-effective design points. To solve this problem, the third generation non-dominated genetic algorithm (NSGA-III) is adopted. The efficiency and accuracy of whole computations are improved by involving BPNN models and NSGA-III algorithm. The proposed method has a good performance in locating the balanced design point between safety and construction cost. Moreover, the proposed method can provide design points with reasonable stiffness distribution.

Pixel design method for deformable structures based on gyroid and topology optimization

Due to the outstanding mechanical properties of gyroid structures, the design of cellular structures based on gyroid lattices and topology optimization is currently a prominent research area in the field of additive manufacturing structural design. Stiffness topology optimization is commonly used in these designs, which improves the stability during specific loadings and the continuity of structures. However, there seems to be little discussion on manufacturing deformable cellular structures based on topology optimization for deformation. This topic has significant value in functionally graded material and programmable soft robotics design. In this work, a hyperelastic material is utilized to construct deformable gyroid lattices. The homogenization method is used to establish a database of variable-stiffness gyroid lattices with varying relative densities. The feasibility of guiding structural deformation through stiffness distribution is proved, and a pixel design method for deformable structures is proposed. In this work, the average normalized stiffness coefficient (ANSC) distribution is calculated by pixelating stiffness distribution. The soft gyroid lattices are used to fill up the design domain according to the ANSC distribution. Finally, two deformable structures, a cloaking metamaterial, and a compliant plier are analyzed to demonstrate the practicality of the proposed method.

Material stiffness optimization for homogenizing contact stress distribution based on particle swarm optimization using elite opposition-based learning mutation

Rapid advances in computer science and material science have made intelligent algorithms promising for solving material design problems. Particle swarm optimization (PSO) algorithm, as a typical swarm intelligence algorithm, is utilized in this paper as the tool to solve the problem of material stiffness optimization for homogenizing the contact stress distribution. In order to achieve an effective and efficient solution, the opposition-based learning (OBL) technique is introduced and combined with PSO to increases its exploration ability. Two mutation strategies, namely, dimension-by-dimension opposition-based learning and multi-dimensional random opposition-based learning mutation strategies, are further proposed to increase the population diversity of PSO. On this basis, algorithms named DEOBL-PSO and MREOBL-PSO are developed. The developed DEOBL-PSO and MREOBL-PSO are then applied to the field of nonlinear contact in engineering, and the specific problem of material stiffness optimization for homogenizing the contact stress distribution is solved. Impressive results are obtained. The contact stress distributing uniformity is substantially improved by material stiffness optimization using DEOBL-PSO and MREOBL-PSO. Additionally, new relation between material stiffness distribution and contact stress distribution is observed, and the effect of the material stiffness variation range on the contact stress distribution is further explored.

Optimization design method of material stiffness of contact interface considering surface roughness for improving thermal contact performance

The contact interface of precision mechanical equipment, such as electronic equipment, is the crucial medium for transferring internal loads and physical properties and realizing the intended function of the equipment. The thermal contact performance of precision mechanical equipment determines its overall thermal performance. Previous studies have consistently ignored the activeness of differential distribution of contact interface material stiffness in improving thermal contact performance. Therefore, this paper creatively proposed a new idea to improve thermal contact performance by designing the material stiffness of the contact interface. Firstly, based on the precise analysis model of thermal contact performance considering surface roughness, a heuristic-based optimization design method of material stiffness of contact interface was developed, which took the contact interface temperature distribution non-uniformity (CITDN) and thermal contact resistance (TCR) as the optimization objectives. Then, based on this method, the optimization designs of electronic chip packaging and proton exchange membrane fuel cell (PEMFC) were carried out. The results showed that after optimization, the TCR and CITDN of the electronic chip package were reduced by 83.23% and 92%, respectively, and the TCR and CITDN of PEMFC were decreased by 99.78% and 88.71%, respectively. This method achieved a substantial improvement in thermal contact performance.

Rigid-flexible coupling modeling of the dual-rotor system for aero-engine

The dual-rotor system is the core component of advanced aero-engine. Establishing a reasonable, accurate, and efficient dynamics model is the key to studying the dynamics and vibration of the rotor system for aero-engine. This manuscript takes a representative aircraft engine dual-rotor system as a prototype, considers the rig-id-flexible coupling characteristics of different stiffness elastic supports and rotor structures, and establishes an analytical dynamic model of the dual-rotor system. Based on the established dynamic model, the natural char-acteristics of the dual-rotor system are analyzed. The model was validated using two different research methods: the rigid-flexible coupling multi-body system dynamics simulation platform ADAMS, and finite element analy-sis. The dynamic model of the dual-rotor system established in this paper can meet the requirements of hierar-chical rigid-flexible coupling of system and structure, overall mass distribution, and stiffness distribution. In particular, it can also effectively realize the simulation of multi-facet and multi-phase unbalanced vibration of the rotor system. The research methods of this paper can further enrich the basic theory of dynamics and vibration of the aero-engine rotor system.

Emulation Evaluation of Interior Beam-Column Connections in PC and RC Moment-Resisting Frames.

Precast concrete (PC) structures have many advantages, but their use in the construction of middle- to high-rise buildings is limited. The construction of PC structures requires skills in various operations such as transportation, assembly, lifting, and structural soundness. In particular, regarding the seismic design of PC structures, it is necessary to clearly evaluate whether they have the same structural performance and usability as integral RC (cast-in-place) structures. In this paper, an experimental study was conducted to investigate whether PC members can achieve a seismic performance equivalent to that of RC members in beam-column joints, which are representative moment-resisting frames. The main variables are the two types of structural systems (intermediate and special moment-resisting frames) and the design flexural strength ratio of the columns and beams. The experimental and analytical results showed that the seismic performance of the PC specimens was equivalent to that of the RC specimens in terms of strength, stiffness, energy dissipation, and strain distribution, except for the specimen with splice sleeve bond failure of the column reinforcement (poor filling of the internal mortar). In addition, the I series satisfied the present emulation evaluation criteria for special moment-resisting frames of PC structures, confirming the possibility of applying intermediate moment-resisting frames.

Detection, localisation and quantification of stiffness loss in a bridge using indirect drive-by measurements

Drive-by health monitoring uses the measurements gathered on a vehicle while traversing a bridge to assess its condition. To date, drive-by monitoring has been mostly proposed as a pre-screening tool to detect damage under favourable conditions of low vehicle speeds and low road roughness. A major shortcoming is the potential degradation of the road profile, which is often indistinguishable from bridge damage. In this paper, the influence of vehicle dynamics, speed and road roughness is removed by applying cross-entropy optimisation to the response of individual crossings of the vehicle at different speeds. The proposed model-based algorithm locates and quantifies damage while remaining unaffected by changes in the road profile. In addition to providing the distribution of bending stiffness in the underlying bridge, the algorithm isolates the bridge deflections accurately making the reconstruction of the actual road profile on the bridge possible. The latter can be a useful feature for ensuring traffic safety as well as preventing a major dynamic amplification of the bridge response. The algorithm is successfully tested for a quarter-car driving on a 15 m simply supported beam bridge model at highway speeds of 30 m/s over a class ‘B’ road with a roughness coefficient of 64 × 10−6 m3/cycle.

Numerical modelling of moment-transmitting timber connections

In recent years, the use of timber in construction substantially increased due to the material’s renewable nature, lower climate impact and increased economic competitiveness. Another driving factor is great improvements in modelling techniques for the design of timber structures. Suitable prediction of the connection behaviour, as a fundamental part of the structural behaviour of timber structures, is crucial for a more economic and reliable design. However, the more realistic and complete connection models, the more complex and difficult to handle they are, which might hinder their practical application. A good trade-off between complexity and computational efficiency can be achieved with the so-called Beam-On-Foundation (BOF) method, which is applied herein in a 2-step hierarchical model to analyse and predict the rotational stiffness, ductile capacity and load distribution among fasteners of four different configurations of moment transmitting beam-to-column timber-to-timber connections. The connection model is validated with experiments on the global response of the connection as well as with a 3-D solid FEM model. The herein proposed connection model well predicted the overall connection response and provided insight into the local fastener behaviour. As compared to the 3-D solid model, which additionally gives access to more realistic local stresses in the timber, the 2-step model is however much more efficient with a great reduction of computation time. This makes the approach suitable for parametric studies and the analysis and engineering design of timber structures.

Spatial distribution of stiffness between and within muscles in paretic and healthy individuals during prone and standing positions

This study investigated the inter- and intramuscular variability of plantar flexors stiffness during prone and standing positions at different muscle lengths in healthy and paretic individuals. To access tissue stiffness, shear wave elastography (SWE) measurements were carried out on two groups: control group (CG; n=14; age 43.9±9.6 years; body mass index [BMI]=24.5±2.5 kg/m2) and stroke survivor group (SSG; n=14; age 43.9±9.6 years; BMI=24.5±2.5 kg/m2). Shear Modulus (μ, kPa) within three plantar flexors (the gastrocnemius medialis [GM], gastrocnemius lateralis [GL], and soleus [SOL]) was obtained during two conditions: prone and standing position, at different angles of dorsiflexion (0°, 10°, and 20°). Measurements were also performed in different proximo-distal regions of each muscle. Muscle activation of the GM, GL, SOL, and tibialis anterior were evaluated during the two conditions. Results showed a high spatial stiffness variability between and within plantar flexors during dorsiflexion. The highest stiffness was observed in the GM, especially in the distal region at 20° in healthy and paretic muscles. In the prone position, the paretic muscle exhibits greater stiffness compared to the healthy muscle (p < 0.05). In contrast, in the standing position, an increase of stiffness in the healthy muscle compared to the paretic muscle was observed (p < 0.05). Thus, mechanical properties are differently affected by stroke depending on active and passive states of ankle muscles during dorsiflexion. In addition, the modification of ankle muscle state change stiffness distribution between and within plantar flexors.

Distributed bending stiffness estimation of bridges using adaptive inverse unit load method

Bending stiffness has important applications in bridge damage detection, model updating, and load bearing capacity assessment. However, accurately predicting bending stiffness is a challenging task. In this paper, a two-phase methodology named the adaptive inverse unit load method (AIULM) is developed for distributed reconstruction of bending stiffness from onboard deflection data. In the first phase, the bending stiffness is roughly estimated by uniform discretization. A global stiffness smoothing method is applied to eliminate nonphysical discontinuities of stiffness at interelement boundaries. Then, the smoothed results are applied in the second phase to define a node optimization function to adaptively adjust the element node distribution. An accurate bending stiffness distribution is provided by performing AIULM analysis again based on optimized discretization. Since only real bridge deflection influence lines (DILs) are utilized in the formulation, the AIULM provides a C0-continuous stiffness distribution without any information on internal force. The adaptive optimization of the node distribution allows the practical application of AIULM to different bridges, especially old bridges. Numerical and experimental validation cases, which demonstrate the excellent predictive capability and practical usefulness of the AIULM, have been performed.

Investigation of reasonable shock absorption of asymmetric long-span suspension bridges considering force differences

Compared with conventional suspension bridges, asymmetric long-span suspension bridges exhibit significant differences in the forces of key members on different sides under earthquake action, due to their uneven mass and stiffness distributions. In this study, the seismic response characteristics of an asymmetric long-span suspension bridge were analyzed using the Guangdong Xijiang Special Bridge as a case study. The shock absorption laws of the asymmetric parameter combinations of the viscous dampers for each control target were investigated. Accordingly, a response surface model for each control objective was established based on the response surface method. The objective function was constructed based on the principle of reducing the differences in multi-target seismic responses on different sides. Finally, a particle swarm optimization algorithm is used to determine the optimal combination of parameters for the viscous dampers on both sides. The results show that the seismic response of the members on the higher-mass side is more evident for an asymmetric long-span suspension bridge under earthquake action. Members on the smaller-mass side have a better shock absorption effect. After optimization using the proposed method, the average optimization magnitude of each control objective reached 23.1%, compared with the traditional symmetric parameters. The optimal combination of the asymmetric parameters of the viscous dampers on both sides can equalize the full-bridge forces and improve the shock-absorption effect of the dampers. The proposed method has a referable meaning for shock absorption control of asymmetric structures.

Multi-level dynamic responses of blast-loaded orthogrid stiffened panels

In this study, the multi-level dynamic responses of the blast-loaded orthogrid stiffened panel (BOSP) is analyzed using the energy method. The dynamic response of the area of panel enclosed by the stiffeners can be considered as the combination of the overall deformation of the neural surface and the local deformation relative to the neural surface. The relevant vibration amplitude is calculated through the Lagrange principle. The theory is verified by the finite element method (FEM). Parametric analysis reveals the effect of the thickness of the panel and stiffener distribution on the dynamic response of BOSP, including the deformation mode and maximum deflection. The anti-explosion theory of BOSP can help effectively predict the deflection, which can guide the ultra-lightweight design of BOSP.

Flutter Optimization of Large Swept-Back Tri-Wing Flight Vehicles

The aerodynamic configuration of large swept-back tri-wings is generally adopted for hypersonic vehicles, but the structural stiffness of the ailerons is weak, which may lead to damage due to the flutter behavior. In the initial stage of structural design, studying the flutter characteristics of tri-wing flight vehicles is necessary and can provide the stiffness index of the tri-wing structural design. To assess the flutter characteristics of tri-wing flight vehicles efficiently, a rapid modeling technique of the finite element method was used in this paper. For the structural scheme of large swept-back tri-wing flight vehicles, a structural dynamic model was modeled using the rapid modeling technique, the unsteady aerodynamic was computed using the double-lattice method, and the flutter characteristics were analyzed using the P-K method. Variable parametric studies were conducted to evaluate the effects of the stiffness of the aileron skin, the stiffness of the control mechanism, and the mass distribution of the aileron on the flutter characteristics of large swept-back tri-wing flight vehicles. The results showed that the key flutter coupling modes of such vehicles are symmetric and anti-symmetric combinations of aileron rotation and torsion. Additionally, optimizing the control mechanism stiffness and mass distribution of the aileron could improve the flutter boundary, which can be helpful in the structural design of such vehicles. The flutter optimization technique effectively improved the flutter boundary, significantly enlarged the flight envelope, and accurately provided the stiffness index for the structural design of large swept-back tri-wing flight vehicles.

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.

Directional Cell Migration Guided by a Strain Gradient.

Strain gradients widely exist in development and physiological activities. The directional movement of cells is essential for proper cell localization, and directional cell migration in responses to gradients of chemicals, rigidity, density, and topography of extracellular matrices have been well-established. However; it is unclear whether strain gradients imposed on cells are sufficient to drive directional cell migration. In this work, a programmable uniaxial cell stretch device is developed that creates controllable strain gradients without changing substrate stiffness or ligand distributions. It is demonstrated that over 60% of the single rat embryonic fibroblasts migrate toward the lower strain side in static and the 0.1Hz cyclic stretch conditions at ≈4% per mm strain gradients. It is confirmed that such responses are distinct from durotaxis or haptotaxis. Focal adhesion analysis confirms higher rates of contact area and protrusion formation on the lower strain side of the cell. A 2D extended motor-clutch model is developed to demonstrate that the strain-introduced traction force determines integrin fibronectin pairs' catch-release dynamics, which drives such directional migration. Together, these results establish strain gradient as a novel cue to regulate directional cell migration and may provide new insights in development and tissue repairs.

Fusion of Magnetic Resonance Elastography Images With Computed Tomography and Magnetic Resonance Imaging Using the Human Visual System.

Magnetic resonance elastography (MRE) is used to assess the stiffness of the liver to rule out cirrhosis or fibrosis. The image, nevertheless, is regarded as shear-wave imaging and does not depict any anatomical features. Multimodality medical image fusion (MMIF), such as the fusion of MRE with computed tomography (CT) scan or magnetic resonance imaging (MRI), can help doctors optimize the advantages of each imaging technique. As a result, perceptions serve as valid and valuable assessment criteria. The contrast sensitivity function (CSF), which describes the rates of visual contrast sensitivity through the changing of spatial frequencies, is used mathematically to characterize the human visual system (HVS). As a result, we suggest novel methods for fusing images that use discrete wavelets transform (DWT) based on HVS and CSF models. Images from MRI or CT scan were combined with MRE images, and the outcomes were assessed both subjectively and objectively. Visual inspection of merging images was done throughout the qualitative analysis. The CT-MRE fused images in all four datasets were shown to be superior at maintaining bones and spatial resolution, despite the MRI-MRE being better at exhibiting soft tissues and contrast resolution. It is clear from all four datasets that the liver soft tissue in MRI and CT images mixed successfully with the red-colored stiffness distribution seen in MRE images. The proposed approach outperformed DWT, which produced visual artifacts such as signal loss. Quantitative evaluation using mean, standard deviation, and entropy showed that the generated images from the proposed technique performed better than the source images and DWT. Additionally, peak signal-to-noise ratio, mean square error, correlation coefficient, and structural similarity index measure were employed to compare the two fusion approaches, namely, MRI-MRE and CT-MRE. The comparison did not show the superiority of one approach over the other. In conclusion, both subjective and objective evaluation approaches revealed that the combined images contained more information and characteristics. Hence, the proposed method might be a useful procedure to diagnose and localize the stiffness regions on the liver soft tissue by fusion of MRE with MRI or CT.