Structural Stiffness Research Articles

An analytical method for determining the rational position of joint section in steel-concrete hybrid girder bridges

The steel-concrete hybrid girder bridge is a structural form that integrates steel and concrete members in the longitudinal direction of the bridge. A critical parameter in designing such bridges is determining the position of the steel-concrete joint section within the main span (in other words, the rational length of the steel portion in the main span). Up to now, previous studies on determining the rational position of joint sections in steel-concrete hybrid bridges have primarily focused on analyses of internal forces and support reactions. However, there is still a lack of research on the rational position of joint section with its relationship to the smoothness of the steel-concrete joint. The distinct material discontinuity, abrupt change in stiffness and complex structure at the joint result in angular deformations, potentially inducing vibrations and stress issues within the bridge structure. To reduce angular deformations, this paper proposes the concept of equal rotations at the steel-concrete joint, ensuring that the rotational angles at both ends of the steel-concrete joint in a hybrid girder are equivalent. Based on this concept, a method for selecting the optimal length of the steel portion in steel-concrete hybrid girder bridges is proposed and validated through nine case studies. Furthermore, several methods are provided to improve the smoothness of the joint between the steel and concrete members. Finally, the proposed approach is applied to the preliminary design of steel-concrete hybrid girder bridges, demonstrating its effectiveness and efficiency.

Growth, first-principles calculations and optical properties of a novel near-infrared Ho: NLGW laser crystal

A rigid structure was constructed using an isotopic doping strategy, and a novel near-infrared 1 at% Ho3+: NaLa0.93Gd0.06(WO4)2 (Ho: NLGW) laser crystal with a size of Φ 18 mm × 30 mm was successfully grown by the Czochralski method. X-ray rocking curves and Rietveld refinement indicate that the grown crystal possesses high crystalline quality and crystallizes in the I41/a space group with lattice parameters: a = b = 5.3518 Å, c = 11.6438 Å and V = 333.5051 Å3. The Ho: NLGW crystal exhibits a low coefficient of thermal expansion (8.472 × 10−6 K−1), and the c-axis thermal conductivity increases from 1.235 W/(m × K) to 1.404 W/(m × K). The thermal properties of the Ho: NLGW crystal surpass those of other Ho3+-doped tungstate series and mainstream near-infrared laser crystals, suggesting that it is easier to obtain excellent laser gain. For revealing the excellent thermal properties, the elastic moduli of the NLW and NLGW crystals have been calculated by first principles. With the introduction of Gd3+, the structural stiffness of the NLW as a whole has been increased to optimize the mechanical properties in each axial direction and to obtain the reason for the larger Debye temperature. Finally, the transmission, absorption and near-infrared emission spectra of the Ho: NLGW crystal were investigated. The crystal exhibits a high transmittance of 88.5 % and an emission cross-section of 0.84 × 10−20 cm2 calculated according to the J-O theory. Experimental results indicate that the grown Ho: NLGW crystal can achieve large laser output more easily and are expected to be an excellent medium for 2 μm solid-state lasers.

Prediction of automotive body-in-white distortion in paint baking process

Thermal-induced distortion prediction of thin shell structures is a challenging task. It often involves highly nonlinear buckling behaviour, where the critical buckling temperature and post-buckling deformations are very sensitive not only to structural stiffness and boundary conditions but also minute geometric imperfections (a.k.a., “surface quality”) of the incoming parts. In the present work, novel Computer Aided Engineering (CAE) methods were developed to predict the thermal-induced distortion of automotive Body-in-White (BIW) panels during paint shop oven-baking processes. The CAE methodology consist of a set of three Finite Element Analysis (FEA) procedures, i.e., thermal-buckling mode analysis, thermo-structural analysis, and imperfection analysis. Two vehicle level case studies showed that simulations successfully predicted the thermal-induced distortion for panels such as the Body Side Outer (BSO) header. It was concluded that the distortion depends primarily on the temperature difference between the BSO and the rest of the BIW during the oven-baking process, rather than the temperatures themselves. Body panel forming quality (e.g., residual stresses and thickness thinning) and assembly dimensional quality were also found to impact the distortions.

Moisture effects on the transverse compressive behaviour of single flax fibres

Studying the effects of moisture on the mechanical behaviour of single flax fibres, particularly in the transverse direction, is of key importance for the reliable use of biobased composites exposed to varying humidity levels. In this study, the apparent transverse Young’s modulus evolution of single flax fibres is recorded through repeated compressive load/unload cycles conducted at three Relative Humidity (RH) levels— 40%, 60%, and 80%. No significant changes in the apparent Young’s modulus, determined from the unloading, were observed during transverse compression cycling or under increasing humidity conditions. The absence of apparent softening with the rise in RH is attributed to the expression of two antagonistic mechanisms: wall softening due to plasticisation and structural stiffening linked to fibre compaction. Intriguingly, a noteworthy transverse stiffening is recorded at 40% RH following the humidification and drying of the fibre. This outcome is ascribed to a hornification phenomenon.

Vortex-induced vibration and energy harvesting of cylinder system with nonlinear springs

Vortex-induced vibration is a common fluid–structure coupling phenomenon in ocean engineering. As a nonlinear stiffness structure caused by anisotropic deformation and support gap, nonlinear spring is of great significance in the field of vortex-induced vibration. Based on the structural dynamics equations and the wake oscillator model, the vibration model of the 2-Degree of Freedom cylinder system with the nonlinear stiffness spring is established. The stiffness ratio, mass ratio, and damping ratio of the cylinder system are changed, and the amplitude and frequency response are analyzed to obtain the effect of nonlinear spring on vortex-induced vibration. The results show that the cylinder system with a nonlinear stiffness spring can maintain a high vibration amplitude in a large Reynolds number range, and the smaller the mass ratio, the more significant the effect is. When m*=1.5, the amplitude of the cylinder system in a cross flow is greater than 0.6 at Re = 180 000–480 000. The energy harvesting in the vortex-induced vibration of cylinder systems with nonlinear stiffness springs is also studied. The efficiency depends on the damping ratio and Reynolds number. When the damping ratio is constant, the energy harvesting efficiency increases first and then decreases with the Reynolds number increases. When m*=1.5, the energy harvesting efficiency of the cylinder system is 19.27% with Re= 35 000 and damping ratio ξ=0.155. As a kind of renewable energy, energy harvesting in vortex-induced vibration is a potential development direction in the future energy field.

On the nonlinear mechanics of hybrid skew aerospace structures

This study proposes a functionally graded (FG) nanocomposite hybrid skew plate element which is fabricated from a polymeric matrix and is reinforced with two well-known nanoscale reinforcements, namely, carbon nanotubes (CNTs) and graphene platelets (GPLs). The Mori–Tanaka approach, the Halpin-Tsai scheme and standard rule of mixtures are employed to estimate the effective mechanical properties of the hybrid plates. To model this structural element, Reddy's third-order shear deformation theory (TSDT) is used. By considering the von-Kármán assumptions and using the Hamilton's principle, the nonlinear static bending and free vibration governing equations are determined. Then the isogeometric analysis (IGA) is employed to establish the structural stiffness and mass matrices of the skew hybrid plates. After validating the correctness of the presented solution procedure with the previously published results, the effects of various variables such as number of layers, distribution pattern of reinforcements (CNTs and GPLs) and their volume fractions, skew angle and width-to-thickness ratio are investigated. It is found that with considering nonlinear von-Kármán relationship in the strain field, the distributions of σxx and σyy about the mid-plane are no longer symmetric.

Quantitative method for the probability of structural damage based on moment theory

In the context of uncertainty in the inverse problem of damage identification, this study proposes a moment theory based probabilistic damage identification (MbPDI) method. Noise errors in the identification process are treated as uncertain parameters, while structural stiffness parameters are treated as functions of noise errors. A limit state function for damage identification is defined, and its probability is computed. Utilizing the concept of moment theory, the expansion series is performed for the limit state function around the most probable point of failure, with gradient information derived using sensitivity matrices. Based on the gradient information and uncertainty inputs, damage probabilities for various elements can be obtained. Additionally, this paper addresses the calculation of structural damage probabilities under the non-normal distribution of random variables by transforming non-normal variables into equivalent normal variables. The proposed probability index and expected index of structural damage in the probabilistic damage identification method has a clear physical meaning, and the calculation has high accuracy. The proposed method is validated through a mathematical example and a numerical simulation. Meanwhile, the influence of damage extent, noise level, and modal order on identification results are analyzed. Experimental validation of the method is also presented.

A starfish-inspired 4D self-healing morphing structure

Inspired by the starfish's unique ability to achieve flexibility and posture-holding with minimal energy expenditure, we present a novel bioinspired morphing structure. Our two-component design, consisting of a thermoplastic mesh and elastomeric jacket, effectively mimics the functions of the starfish's ossicles, mutable collagenous tissues, and derma. This structure exhibits a remarkable combination of self-healing, time-dependent shape memory, and self-posture-holding properties. Systematic variations in mesh geometry demonstrate precise control over structural stiffness and thermal response, enabling customization for specific applications. The structure's scalability and ease of fabrication further enhance its adaptability. We experimentally demonstrate the potential of our biomimetic morphing structure using several prototypes. This work lays the foundation for developing a new type of versatile morphing structures with applications in diverse fields, including robotics, biomedical devices, and adaptive structures.

Mechanism of enhanced impulse and entrainment of a pulsed jet through a flexible nozzle

The present experimental study shows that a nozzle with optimal flexibility can enhance the impulse and entrainment of a pulsed jet. Near the nozzle exit, vortex rings emanating from the flexible nozzle move faster because of the timely release of the elastic energy (stored during the expansion) to the jet, which is maximized at the structural stiffness that needs to be optimally tuned to the jet acceleration. The total circulation, hydrodynamic impulse and entrained fluid volume are enhanced substantially. Interestingly, we find that the same condition for optimal flexibility to maximize the hydrodynamic impulse and circulation of the primary vortex ring of the continuous jet (Choi & Park, J. Fluid Mech., vol. 949, 2022, A39) holds universally for the pulsed jet, indicating that abrupt jet termination is irrelevant to the impulse augmentation mechanism. Compared to the rigid counterpart, increments of the impulse ( ${\sim }400\,\%$ ) and entrainment ( ${\sim }220\,\%$ ) of a pulsed jet in the present study are considerably larger than those ( $200\,\%$ and $50\,\%$ , respectively) in a continuous jet from previous studies, which is attributed to the significant suppression of negative pressure at the nozzle exit by the collapsing motion of the flexible nozzle in the phase with the jet-driven upstream propagation of the surface wave on the nozzle. This universal mechanism provides a guideline for a novel jet propulsor using a flexible nozzle, for example, for small-scale underwater robots.

Multi-objective Topology Optimization Design for a Certain Launcher Bracket

To achieve weight reduction and enhance the firing accuracy of a specific type of launch device, the bracket was selected as the optimization subject for multi-objective topology optimization. Single-objective optimization often overlooks other influencing factors. To address the limitations of single-objective optimization, this study adopts the variable density method from the SIMP approach and proposes a multi-objective topology optimization based on compromise programming. This study, through multi-objective topology optimization of the bracket, obtained an optimized topology structure that maximizes static stiffness and the dynamic low-order natural frequencies of the launch device bracket at launch angles of 0°, 53°, and 85°, with an azimuth angle of 0°. Finally, the obtained topology structure was validated using finite element software. The design method presented in this paper not only enhanced the stiffness of the bracket structure for such launch devices and increased the first two natural frequencies of the bracket but also achieved weight reduction. The optimization design process also provides a reference for other mechanical structures.

Exploration of changes in rheological and spectral properties of rice protein inks before and after 3D printing

The aim of this work was to understand the effect of the printing process on food inks by applying the chemometric approach to analyze the rheological and spectral properties of rice protein. Rice protein was printed under two conditions (speed: 35 and 50 mm/s, layer height: 1.5 and 1.2 mm, and nozzle diameter: 1.7 and 1.2 mm). Infrared spectroscopy and oscillatory tests at 1 Pa between 0.1 and 10 Hz were performed before and after printing. PCA and k-means analysis of rheological and spectral data identified patterns and significant differences. The analysis revealed that 3D printing affects rheological properties, reducing structural stiffness and modifying the relationship between elastic and viscous behavior. Spectral vibrations associated with NH, CH3, O-H, and C=O functional groups indicated significant structural changes due to the printing process. These results suggest that the printing process influences food inks' rheological and structural properties.

Mechanism of sucrose improving the mechanical characteristics of foams stabilized by soy protein isolate/gellan gum/guar gum ternary complex

Sucrose shows the potential of stabilizing foam system. This study systematically evaluated the mechanism by which sucrose improved foaming properties and mechanical characteristics of foams stabilized by soy protein isolate/gellan gum/guar gum ternary complex. Results showed that sucrose could bond to the surface of ternary complex or self-aggregate within the continuous phase, resulting in the neutralization of charges (nearly zero) and an increase in particle size (up to 62.54 μm). The addition of 30 % sucrose reinforced foam system with an increased foamability (305.99 %) but a longer foaming time (10 min) during foaming process. Moreover, the mechanical characteristics, including hardness, elastic strength (Power-law constant) and solid characteristic (frequency exponent), were also significantly enhanced to 1.26 N, 354.7956 and 2.5873, respectively, which were 1.65, 1.94 and 1.11 times than those of foams without sucrose. The microscopic mechanism lied in the reduced water freedom degree caused by sucrose, which generated a compact structural network around bubbles for providing a stable and stiff structure to foams. These findings will provide clear theoretical guidance for regulating mechanical characteristics of aerated foods by using sucrose as structural building blocks.

Wind-induced collapse mode and mechanism of super-large hyperbolic steel reticulated shell cooling tower with stiffening rings

With advancement of dry-air cooling technology, it has become feasible to use steel reticulated shell structures in design and construction of industrial cooling towers. Steel reticulated shell cooling towers (SRSCTs) with light weight, high strength, and rapid construction have development potential. Wind-induced collapse accidents in cooling towers frequently occur, characterized by pronounced nonlinear behavior involving significant deformation and material failure. Nevertheless, current stability and collapse analyses of cooling towers based on linear theory and elastic deformation are inadequate and unsafe. Thus, the wind-resistant stability of SRSCTs must be evaluated considering their inherent high flexibility and low damping levels. Considering a 220 m high hyperbolic SRSCT as a case study, a wind-induced collapse FEM simulation and analysis were performed. The average and fluctuating wind loads were measured in a reduced-scale model during wind tunnel tests and used as the time-variant wind pressure in a structural finite-element model. The dynamic performance and buckling collapse analyses of the cooling tower were conducted considering geometric and material nonlinearities. The entire wind-induced failure process of the SRSCT in extreme winds was systematically investigated. The weaknesses in the structural stiffness and the failure process were quantified, with five failure stages and four failure modes. The failure stages included linear elasticity, local member failure, local regional failure, overall structural failure, and collapse. The failure modes included circumferential plastic buckling zone failure, windward buckling failure of the shell, crosswind failure of the stiffening ring (hinged curved-beam mechanism), and windward failure of the stiffening ring (triangular arch-like mechanism). This study confirms that development of plastic buckling zones and formation of plastic hinges, considering geometric and material nonlinearity, are the dominant factor in wind-induced failure and collapse of SRSCTs.

Shear strength of steel-concrete composite I-beams with corrugated steel webs

Corrugated steel webs have been widely applied to steel-concrete composite beams due to their excellent shear performance. However, there needs to be adequate research on the shear behavior of steel-concrete composite I-beams with corrugated steel webs, and the proportional distribution of shear forces between concrete flanges and corrugated steel webs in composite I-beams has yet to be clarified. This paper experimentally investigates steel-concrete composite I-beams with corrugated steel webs with different shear span ratios. With the increase of the shear span ratio, the shear failure mode of the beam gradually evolves from shear-dominated to flexural-dominated, the shear capacity and structural stiffness of the beam are negatively affected, and the improvement of the shear resistance of the beam after webs buckling is gradually limited. As the primary shear component, corrugated steel webs contribute about 71 % to 92 % of the total sectional shear force. Notably, accounting for 15 % to 35 % of the shear capacity of the beam, the shear contribution of the concrete flange must also be typically considered. For the generalizability of research results, parametric studies are conducted using validated numerical models to comprehensively investigate the effects of steel yield strength, concrete strength, web thickness, web height, and shear span ratio. Afterward, an efficient analytical model considering the shear capacity of the concrete flange is proposed to estimate the shear strength of composite I-beams with corrugated steel webs. The proposed analytical model agrees satisfactorily with experimental and numerical analysis results. The research results can provide valuable support for designing and optimizing steel-concrete composite I-beams with corrugated steel webs.

Seismic performance of pentagonal type aluminum alloy suspen-dome structure with large opening

Prestressing technology is an effective way to enhance the mechanical properties of space structures. In view of this, a new pentagonal type aluminum alloy suspen-dome structure with large opening is proposed in this paper by introducing the lower cable support system into the aluminium alloy single-layer reticulated shell structure. The seismic performance of this new structure is investigated using time-procedure analysis. Firstly, the effects of rise-span ratio, thickness-span ratio, prestressing level, horizontal radius factor for lower chord nodes and roof loading on the free vibration characteristics of the structure with different supporting stiffness are investigated. The distributions of internal forces and displacements of members of overall structure considering lower support and roof structure only are analyzed. Subsequently, the dynamic response of the structure under seismic combinations of different dimensions and directions is investigated, and reasonable combinations that should be considered for simplified analyses are derived. Furthermore, seismic internal force coefficients are introduced to assess the degree of seismic effects on various types of members. On this basis, parametric analysis of the seismic performance of the structural performance is conducted and quantitative assessment of the sensitivity of the parameters is carried out. Additionally, the free vibration characteristics and dynamic performance of steel and aluminium suspen-dome are compared. The results show that considering the supporting structure weakens the structural stiffness while increasing the structural dynamic response; reasonable values of key parameters in the seismic design of the structure are obtained; and the rise-span ratio and thickness-span ratio are important influencing factors of the seismic performance of the structure. Besides, the internal forces of members in aluminium alloy suspen-dome are less affected by seismic effects than those in steel suspen-dome, and the new structure has good seismic performance.

3D printing single‐stroke path planning, local reinforcement and performance testing of MBB beams and cantilever beams

Abstract3D printing of continuous fiber reinforced thermoplastic composites (CFRTPCs) has been applied for the molding of composite complex structures due to the advantages of flexibility and one‐step forming. In this study, feature points simplification, merging and rearrangement were accomplished for Messerschmitt‐Bölkow‐Blohm (MBB) beam and cantilever beam to generate single‐stroke print paths for the specimens. For the significant stress areas in the finite element analysis results of these structures, a local reinforcement method using orthogonal layups was proposed, which was achieved by raising and lowering the print head and adjusting the fiber volume fraction during the printing. After experimental validation and failure modes analysis, the path planning significantly improved the peak load and structural stiffness of the specimens, and the local reinforcement further enhanced the equivalent specific strength and specific stiffness. This study provides a single‐stroke 3D printing strategy for complex structure molding in conjunction with parameter adjustments.Highlights A single‐stroke path planning was developed for MBB beams and cantilever beams, including simplification, merging and rearrangement methods for feature points. A local reinforcement method was proposed, which was achieved by raising and lowering the print head and adjusting the fiber volume fraction during the printing process. The effect of different print paths on specimen properties was investigated.

Design, Simulation, and Fabrication of Composite Lattice Orthoses with Enhanced Structural Performance

Abstract Orthoses play a critical role in rehabilitation by providing fracture stabilization, external load protection, and deformity correction. Traditional methods of orthotic manufacturing often result in reduced breathability leading to potential skin problems, and increased bulkiness and weight due to material and processing limitations. Method: This study aims to enhance breathability and structural performance of orthoses through the utilization of a fiber-reinforced composite lattice design fabricated using a Coreless Filament Winding (CFW) process. An arm brace was designed and manufactured, which incorporates four modules made of fiberglass/polystyrene composite lattices assembled together using adjustable thermoplastic connectors. To simulate the structural performance, a Finite Element Model (FEM) was constructed with careful consideration of the interactions between the connectors and the lattice modules, and this was subsequently validated through experiment. Results: In comparison to a benchmark brace made of Polylactic Acid (PLA) lattice, the composite brace exhibits a significant reduction in thickness (60%) and weight (44%) while maintaining equivalent structural performance. The validation test indicates the FEM's reliability in predicting structural stiffness and strength, with the predicted peak loading being slightly conservative (5%) compared to experimental results. Conclusion: Composite lattice structures represent a significant advancement in the design of breathable, lightweight, and high-strength orthoses. Moreover, the developed FEM serves as a valuable tool for accurately predicting structural performance and optimizing orthotic design under varying loading conditions.

Copper‐graphene coatings for improving thermal shielding of CFRPs through electrodeposition techniques

AbstractToday, carbon fiber reinforced plastics (CFRPs) are materials of interest several industrial sectors because of their mechanical properties and low weight. However, applications in high‐temperature areas are limited because of thermal degradation. Thus, thin coatings acting as thermal shielding and ensuring the upkeep of CFRP structural stiffness are of high interest. This work presents an innovative approach to produce copper/graphene bilayer coatings through electrodeposition and electrophoretic deposition; it consists of laser pre‐treatment of the composite surface to remove the matrix layer exposing the carbon fibers, enabling the subsequent deposition. Bi‐layer graphene/copper coatings exhibit an enhancement in copper electrodeposition efficiency of more than 59% resulting in a 97% stiffness improvement compared to the single layer copper electroplating. All the obtained coatings were able to act as a thermal shield of the CFRPs, reducing the maximum temperature of the composite by more than 60%. In particular, due to the synergistic effect of copper and graphene, the GNPs‐Cu coating achieved the highest maximum temperature reduction (81%). Cross‐sectional analysis indicates severe delamination in uncoated CFRPs, whereas double‐layer coatings maintain structural integrity and prevent delamination even under high‐energy exposure. In addition, the coated composites exhibit a higher electrical conductivity compared to the laser cleaned CFRP, with the GNPs‐Cu coating that obtained a 90% enhancement because of the outstanding electrical properties of copper and graphene.Highlights The laser cleaning pretreatment allows the electrodepositions on CFRPs. The GNP‐Cu scenario achieves the highest deposition efficiency. A 97% stiffness improvement was achieved by GNPs‐Cu scenario. GNPs‐Cu coatings exhibit the utmost reduction in resistivity (98%). The GNPs‐Cu coating achieves the highest thermal shielding performance (81%).

Stiffness properties of regular p-bars tensegrity prisms under the compressive loading

The regular tensegrity prisms are a kind of fundamental unit, which can be formed into different configurations by different splicing approaches to achieve specific structural functions. Taking regular prisms as the research object, this article presents an analytical method for structural deformations under compressive loading. The structural parameters after loading can be obtained directly by solving the nonlinear force density equation, which simplifies the form-finding process. This article also studies the structural stiffness under different connection modes. By defining the twist angle change rate and internal force utilization rate, we can compare the relative deformation of different tensegrity prisms. The results show that the relative deformation of the three-bar prism is minimal, and it has the best stiffness.

A custom pipeline for building computational models of plant tissue

Stalk lodging in the monocot Zea mays is an important agricultural issue that requires the development of a genome-to-phenome framework, mechanistically linking intermediate and high-level phenotypes. As part of that effort, tools are needed to enable better mechanistic understanding of the microstructure in herbaceous plants. A method was therefore developed to create finite element models using CT scan data for Zea mays. This method represents a pipeline for processing the image stacks and developing the finite element models. 2-dimensional finite element models, 3-dimensional watertight models, and 3-dimensional voxel-based finite element models were developed. The finite element models contain both the cell and cell wall structures that can be tested in silico for phenotypes such as structural stiffness and predicted tissue strength. This approach was shown to be successful, and a number of example analyses were presented to demonstrate its usefulness and versatility. This pipeline is important for two reasons: (1) it helps inform which microstructure phenotypes should be investigated to breed for more lodging-resistant stalks, and (2) represents an essential step in the development of a mechanistic hierarchical framework for the genome-to-phenome modeling of herbaceous plant stalk lodging.