Initial Curvature Research Articles

Sensitivity analysis for sectional stiffness of anisotropic beams: The direct and adjoint methods

This paper concerns with the determination of sectional stiffness matrix and its sensitivity for anisotropic beams with initial curvatures. The governing equations of a three-dimensional beam is formulated to a Hamiltonian system, and the reduction of the Hamiltonian matrix leads to a set of singular, linear equations of the sectional warping and compliance matrix. The left and right null spaces of the singular linear system are explicitly constructed, and the existence and uniqueness of sectional warping and compliance matrix are justified. The direct and adjoint methods for sensitivity analysis of sectional stiffness matrix are developed. The existence and uniqueness of solutions for singular equations resulting from the direct and adjoint methods are proved formally. Numerical examples are presented to validate the proposed methods. The predictions of sensitivities from the direct and adjoint methods are shown to agree well with results of the complex-step method.

Research on methylene blue degradation based on multineedle-to-plane liquid dielectric barrier discharge mode

Advanced oxidation processes (AOPs) focusing on non-thermal plasma induced by dielectric barrier discharge (DBD) are adequate sources of diverse reactive oxygen species beneficial for water and wastewater treatment. The degradation of methylene blue (MB) was investigated using plasma liquid dielectric barrier discharge with a multineedle-to-plane reactor. MB at 20 mg/L concentration was almost completely degraded after 40 min of treatment. In this study, several important parameters, such as input voltage, initial concentration, initial pH, discharge gap, tip radius of curvature, and presence of radical, were evaluated, and their effects on MB degradation rate were investigated. The degradation rate of MB increased with initial pH. By contrast, the degradation rate showed a downward trend with increasing initial concentration, discharge distance, and tip curvature radius. O3 and H2O2 produced during the degradation process considerably influenced the entire degradation process, especially when the quenching agents of HO⋅, O2·- and e− were added, and the degradation efficiency was obviously reduced. According to the measured spectrum, the possible process of the discharge process was analyzed, and the COMSOL finite element simulation is performed to obtain the visualization of the discharge model. This work can provide exploratory platforms for comprehensively understanding and enhancing MB degradation in DBD plasma technology.

Does relativistic cosmology software handle emergent volume evolution?

Several software packages for relativistic cosmological simulations that do not fully implement the Einstein equation have recently been developed. Two of the free-licensed ones are inhomog and gevolution. A key question is whether globally emergent volume evolution that is faster than that of a Friedmannian reference model results from the averaged effects of structure formation. Checking that emergent volume evolution is correctly modelled by the packages is thus needed. We numerically replace the software's default random realisation of initial seed fluctuations by a fluctuation of spatially constant amplitude in a simulation's initial conditions. The average volume evolution of the perturbed model should follow that of a Friedmannian expansion history that corresponds to the original Friedmannian reference solution modified by the insertion of the spatially constant perturbation. We find that inhomog allows emergent volume evolution correctly at first order through to the current epoch. For initial conditions with a resolution of $N = 128^3$ particles and an initial non-zero extrinsic curvature invariant $I_i = 0.001$, inhomog matches an exact Friedmannian solution to -0.00576% (Einstein-de Sitter, EdS) or -0.00326% (LCDM). We find that gevolution models the decaying mode to fair accuracy, and excludes the growing mode by construction. For $N = 128^3$ and an initial scalar potential $\Phi$ = 0.001, gevolution is accurate for the decaying mode to 0.0125% (EdS) or 0.0125% (LCDM). We conclude that this special case of an exact non-linear solution for a perturbed Friedmannian model provides a robust calibration for relativistic cosmological simulations.

Clinical aspects of cervical spine traumatic injury biomechanics

Cervical spine trauma is one of the most serious injuries of the human musculoskeletal system, as structural disorders of the cervical spine lead to neurological disorders due to damage to the spinal cord and/or its roots or create conditions when instability poses a significant potential threat to anatomical integrity and functional capacity of the spinal canal structures. A lot of classifications of traumatic injuries of the cervical spine have been developed, they are based on the biomechanics of injury, but none of them is generally accepted and universal. Failures to develop a system that could clearly determine the causal relationship between the effects of the traumatic agent and the traumatic bone changes are due to a number of causes. Extensive clinical material accumulated over the years of study of traumatic changes in the cervical spine allowed identifying the main criteria that determine the nature and degree of traumatic injuries. These include the parameters of traumatic action and individual characteristics of the victims, in particular physiological indicators and the presence of comorbidities. In this review, we present a brief description of the main clinical factors influencing the biomechanics of traumatic cervical spine injury (nature, direction and intensity of traumatic action, age of a patient, muscle condition and initial curvature of the cervical spine, as well as some comorbidities: degenerative changes of the spine, osteoporosis, connective tissue diseases, congenital malformations). These criteria are of practical importance that allows using the collected information not only in theoretical but also in applied aspects.

Performance characterization of transparent and conductive grids one-step-printed on curved substrates using template-guided foaming.

Next-generation electronic devices require electrically conductive, mechanically flexible, and optically transparent conducting electrodes (CEs) that can endure large deformations. However, patterning conditions of such CEs have been mainly limited to flat substrates because of the nature of conventional fabrication techniques; thus, comprehensive studies are needed to be conducted on this topic. Herein, we characterize the material and structural properties of CEs, curvature of substrates, and their operational performance. We use a single-step printing method, termed template-guided foaming (TGF), to fabricate flexible transparent conducting electrodes (FTCEs) on various substrates with initial curvatures. We adopted silver nanowires (AgNWs) and a conductive polymer (PEDOT:PSS) to characterize and compare the effect of initial substrate curvatures on the sheet resistance during inward and outward bending. The AgNW-based grids exhibited a considerably low sheet resistance, which was linearly proportional to the working curvature of the substrate, whereas PEDOT:PSS-based grids exhibited a relatively higher sheet resistance, which increased regardless of the initial and working curvatures of the substrate. Although both CE grids exhibited a high flexibility and transmittance during 10 000 cyclic tests, the initial curvature of the substrate affected the sheet resistance; hence, operational conditions of FTCEs must be considered to improve the repeatability and durability of such FTCE-integrated devices. Finally, we believe that our study introduces a novel methodology for the design, fabrication, and operation strategy of flexible electronic devices and wearable devices with high performances.

Functional evaluation of height–diameter relationships and tree development in an Australian subtropical rainforest

Context Allometric equations describing the relationships between tree height (H) and breast height diameter (D) should be both statistically efficient and biologically relevant. Aims To determine whether selected allometric equations can meet established criteria for both efficiency and relevance. Methods Nine equations were compared to define the H–D relationships of 1122 individuals and 18 species from an Australian subtropical rainforest. Key results Three-parameter asymptotic equations described initial slope (a), curvature (b), and asymptotic height (Ha). Each equation was evaluated for precision (root mean square error, RMSE) and bias in H estimates, and ease of interpretation of function parameters. For both individual species and all stems, a non-rectangular hyperbola (NRH) provided almost equally high precision and low bias as did the statistically most parsimonious generalised Michaelis–Menten function, plus linear parameter values easily relatable to tree structural and functional attributes. The value of NRH a increased linearly with wood density for canopy species, but not for understorey and subdominant species, whereas the value of NRH b decreased as Ha increased from understorey to canopy species. Conclusions Species within understorey, subdominant, and canopy structural groups shared similar ranges of parameter values within groups that reflect both intrinsic architectural and developmental patterns, and environmental limitations to Ha. Implications The NRH can be used to visualise both early and later tree development stages and differences among the growth patterns of species occupying different positions within a forest.

Second–order models for the bending analysis of thin and moderately thick circular cylindrical shells

The suitability of employing the second-order shear deformation theory to static bending problems of thin and moderately thick isotropic circular cylindrical shells was investigated. Two variant forms of the polynomial second-order displacement models were considered. Both models account for quadratic expansions of the surface displacements along the shell thickness, although the second model (SSODM) was augmented by the initial curvature term. The equilibrium equations were derived by use of the principle of virtual work. Navier analytical solutions were obtained under simply supported boundary conditions. The results of the displacements and stresses revealed that the theory formulated on the SSODM provides a good depiction of the bending response of thin and moderately thick shells and are in close agreement with those of the first and higher-order shear deformation theories (FSDT; HSDT). The ability of the theory formulated on the first model (FSODM) to predict adequate values of displacements and stresses in thin shells was found to be significantly affected by changes in length to radius of curvature (l/a) ratios.

Towards an intelligent straightening system for flat enameled copper wire: problem statement, review of related work, and basic concept

Enameled copper wire is a crucial material for the production of modern electrical machines. With the advent of hairpin windings, copper wire with rectangular cross-section is gaining importance. Being delivered on coil carriers, the wire is subject to initial curvatures which must be leveled out before further processing. Since common straightening systems are set manually and not controlled automatically due to missing sensor feedback, the straightening process is very susceptible to material-related deviations. After providing an in-depth problem statement, this paper gives a structured overview of related approaches and derives a basic concept for the intelligent straightening of flat enameled copper wire.

Coupled dynamics of axially functionally graded graphene nanoplatelets-reinforced viscoelastic shear deformable beams with material and geometric imperfections

This paper is the first to explore the coupled dynamics of geometrically and material-wise imperfect axially functionally graded (AFG) graphene nanoplatelets-reinforced viscoelastic third-order shear deformable beams. Four AFG graphene nanoplatelets distribution patterns are considered. Porosity, as the material imperfection, is modelled using a Gaussian Random Field model. Four thickness-wise functionally graded porosity distribution patterns are modelled. Effects of geometric imperfection are included by assigning an initial curvature to the beam. To consider the influences associated with energy dissipation caused by internal friction, the Kelvin-Voigt model for viscosity is used. External dissipative energy is modelled using a transverse damper. The effective material properties of the AFG beams are calculated using a modified Halpin-Tsai micromechanics model, together with a rule of mixture. Coupled axial, transverse, and rotational motion equations are obtained by employing a Hamiltonian approach and third-order shear deformation. The natural frequencies are obtained using a modal decomposition method. A simplified version of the graphene nanoplatelets-reinforced AFG structure is verified by a computer code-based finite element method. This novel study on the effects of geometrical imperfection on the sensitivity of beams towards porosity imperfections demonstrates the significance of scrutinising the effects of one imperfection on another.

Softening–hardening transition in nonlinear structures with an initial curvature: a refined asymptotic analysis

Softening–hardening transition in nonlinear structures with an initial curvature: a refined asymptotic analysis

Anti-curvature honeycomb lattices for mode-dependent enhancement of nonlinear elastic properties under large deformation

Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. Such lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt straight beams. While a large set of mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. Here we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing the effective elastic moduli in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective elastic moduli of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the deformed shapes corresponding to compressive or tensile modes of the honeycomb cell walls as the initial beam-level configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode, leading to increased effective elastic moduli. Moreover, unlike conventional materials, we demonstrate that it is possible to achieve non-invariant elastic moduli under tension and compression. Within the framework of a unit cell based approach, the cell walls with initial curvature are modeled as curved beams including nonlinear bending and axial deformation, wherein the governing equation is derived using variational energy principle through the Ritz method. The developed physically insightful semi-analytical model captures nonlinearity in elastic moduli as a function of the degree of anti-curvature and applied stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattice materials proposed in the present article introduces novel exploitable dimensions in mode-dependent effective elastic property modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.

Investigation of an electrostatically actuated imperfect circular microplate under transverse pressure for pressure sensor applications

In this paper, we present static and dynamic analysis of an electrostatically actuated imperfect circular microplate under transverse pressure. In modelling of the microplate, we have included both von Kármán geometric and electrostatic force nonlinearities in the development of the equation of motion. The equation of motion has been solved using Galerkin based reduced order modelling technique. The developed reduced order model has been first validated by comparing it with finite element simulation results. Further, the effects of imperfection as initial curvature and uniform transverse pressure have been investigated on the static and dynamic characteristics of the electrostatically actuated circular microplate. We have also investigated the effects of imperfection and applied DC voltage on the pressure sensitivity of the circular microplate. We have found that both imperfection and electrostatic load are responsible for appreciable variations in sensitivity. This detailed investigation is useful to design an imperfect micro pressure sensor.

Experimental–theoretical investigation of the short-term vibration response of uncracked prestressed concrete members under long-age conditions

The short-term vibration response of uncracked prestressed concrete (PC) members under long-age conditions was investigated. No study has examined long-term phenomena of concrete, such as its tendon relaxation, creep, curing, and shrinkage, under the aforementioned conditions. Therefore, a research sub-program was initiated at the National Center for Research on Earthquake Engineering on the basis of an experimental campaign on uncracked PC bridge members initiated in 2015. In particular, a simply supported PC beam composed of a parabolic-bonded tendon and high-strength concrete made in Taiwan was allowed to short and, consequently, long-term prestressing losses measured for approximately 9.5 months. During short-term prestressing losses and after long-term prestressing losses, free short-term transverse vibrations were induced in the PC beam characterized by a second-order initial curvature and an axial end constraint. The time-dependent Young’s modulus of the beam was determined by conducting compression tests on cylinders during the short-term prestressing losses. Moreover, compression tests were conducted on cores drilled along the PC beam’s span after free vibration tests. The theoretical time-dependent Young’s modulus of the beam was evaluated according to the compression test results. The experimental data were compared with a reference Euler–Bernoulli solution and finite-element (FE) model that describe the dynamics of PC girders by considering the effective prestressing force. The fundamental frequencies of the PC beam were mainly sensitive to the variation in its initial tangent Young’s modulus due to the consolidation or hardening of concrete. These frequencies were unaffected by the second-order initial curvature. In conclusion, the reference solution and FE model can accurately predict the short-term dynamics of uncracked PC members exposed for long times.

Outcome Study of Anterior Cervical Discectomy and Fusion with Lordotic Cage Insertion

Objective: This study retrospectively evaluated the clinical and radiographic outcomes following the use of a lordotic cage in anterior cervical discectomy and fusion (ACDF).Material and Methods: All patients who underwent ACDF, at Vajira Hospital; between May 2017 and May 2020, were included in this study. Radiographic images were used to evaluate the device-level Cobb angle (DLCA), segmental Cobb angle (SCA), global Cobb angle (GCA), sagittal vertical axis (SVA), sagittal alignment (SA), and intervertebral disk height. The visual analog scale (VAS) for neck pain, and the Japanese Orthopaedic Association (JOA) score were reviewed as part of the patient’s medical records. Preoperative DLCA, SCA, GCA, SVA, SA, and intervertebral disk height measurements were compared with postoperative measurements at 1 year.Results: A total of 51 patients (88 disks), having undergone ACDF with lordotic cage insertion were included in this study. The initial curvature of the cervical spine was diagnosed as kyphosis in 30 (58.8%) patients, and as lordosis in 21 (41.2%) patients. There was significant improvement in the VAS, JOA, DLCA, SCA, GCA, SVA, SA, and intervertebral disk height after ACDF (p-value<0.050). In patients with preoperative kyphosis, the greatest changes were observed in the GCA (p-value=0.004).Conclusion: The use of a lordotic cage in ACDF improved both the clinical and radiographic outcomes of all postoperative parameters, regardless of the patient’s preoperative cervical spine curvature; although, patients with preoperative kyphosis had greater improvement in GCA.

On the snap-through buckling analysis of electrostatic shallow arch micro-actuator via meshless Galerkin decomposition technique

Micromechanical systems (MEMS) based on electrostatic actuators are commonly involved in driving and actuating high-speed micro-structures. For this to be efficient, these micro-actuators must produce sufficient actuating force in order to achieve the required large strokes for such operations (usually in the order of tens of microns). However, this larger amount of displacement will require high actuation electrostatic voltages (typically in the order of hundreds of volts) or larger actuator dimensions, resulting in a bulky and inefficient design. To overcome these challenges, this paper examines the possible use of the snap-through instability in an electrostatically actuated and initially curved (shallow arch) clamped-clamped microbeam actuator arrangement. An extended version of the variational Hamilton principle is applied to derive nonlinear equations governing the steady-state behavior of the structure under step DC load. These equations are solved by effectiveness meshless numerical Galerkin decomposition technique. A convergence study is performed to show the effectiveness and advantages of the applied numerical approach to the formulated nonlinear problem. The investigation inspects different initial curvature profiles (first three symmetric buckled modes: first, third, and fifth modes) for the shallow arch. It was reported that the presence of the snap-through instability, for all investigated initial profiles, in the structural behavior of the micro-actuator produces a non-trivial order of magnitude increase in its resultant displacement as compared to the classical parallel-plate actuator with identical geometrical dimensions and operating conditions. In addition, out of the assumed first three symmetric buckled modes to outline the initial curvature of the shallow arch microbeam, only the first and fifth modes showed a strong impact on the micro-actuator performances.

Test and theoretical investigation of an improved CFRP-steel tube composite member under axial compressive loading

This paper presents an experimental and numerical study on the mechanical characteristics of an improved CFRP steel tube composite members (CFRP-STCMs) under axial compressive loading. The CFRP-STCM was reinforced with a thick-walled steel tube at both ends to prevent local buckling of CFRP retrofitted equal thickness circular steel tube under axial compressive load. The main focus of the lab test was the effects of fiber winding directions and the test results reveal that the related specimen mainly suffers from overall buckling failure modes. The remaining failure characteristics of the test specimens vary with the change in the fiber winding direction. The longitudinal fiber winding direction has the most obvious reinforcement effect on the load-bearing capacity of the composite member. The ±45° fiber winding direction leads to obvious torsion failure modes after the overall buckling of the test specimen. The numerical modeling was carefully validated using the test results and an extensive parametric analysis was conducted covering a reasonably wide range of geometric configurations. Parameterized numerical analysis reveals that the initial geometric imperfections (initial curvature) and the geometric configurations of the composite member other than the thickness of the adhesive layer have a significant influence on the load-bearing capacity of the composite member. A modified theoretical method for predicting the critical load of the composite member is proposed based on the Perry-Robert stability formula. The proposed simplified formula can accurately predict the critical buckling load of CFRP-STCM with errors and coefficients of variation are −2.71% and −0.014, respectively.

Analysis of the Piezoelectric Properties of Aligned Multi-Walled Carbon Nanotubes

Recent studies reveal that carbon nanostructures show anomalous piezoelectric properties when the central symmetry of their structure is violated. Particular focus is given to carbon nanotubes (CNTs) with initial significant curvature of the graphene sheet surface, which leads to an asymmetric redistribution of the electron density. This paper presents the results of studies on the piezoelectric properties of aligned multi-walled CNTs. An original technique for evaluating the effective piezoelectric coefficient of CNTs is presented. For the first time, in this study, we investigate the influence of the growth temperature and thickness of the catalytic Ni layer on the value of the piezoelectric coefficient of CNTs. We establish the relationship between the effective piezoelectric coefficient of CNTs and their defectiveness and diameter, which determines the curvature of the graphene sheet surface. The calculated values of the effective piezoelectric coefficient of CNTs are shown to be between 0.019 and 0.413 C/m2, depending on the degree of their defectiveness and diameter.

A mechanical model to determine upheaval buckling of buried submarine pipelines

Thermal loads in submarine pipelines generate an axial compressive load that can force the pipeline to buckle, leading to failure if these loads are not considered in the design. Buried pipes are constraint to displacements in all directions, which leads to a high compressive load in the longitudinal axis and makes the pipes more vulnerable to buckling. If buried pipes under thermal loads do not buckle, a high-stresses state takes place when it is combined with high-pressure conditions. In this work, a simple mechanical model to determine the axial buckling load of a buried pipeline is proposed. The model is based on a simply supported beam subjected to a distributed transverse load representing the soil uplift resistance obtained from a referenced model, and an axial compressive load that represents the effective axial force and is computed according to the DNV-RP-F110. Additionally, the pipe–soil system is analyzed through a non-linear finite element model to compare the results with the analytical solution. The proposed simple mechanical model can capture the upheaval buckling behavior and provides results that are consistent with the numerical analysis, specifically for the two main parameters evaluated, namely, the initial pipe curvature and the magnitude of the transverse load.

An updated parametric hysteretic model for steel tubular members considering compressive buckling

An updated parametric hysteretic model for steel tubular members, in which the member compressive buckling is considered, is proposed in this paper. The model can be used for simulating the complex inelastic force-displacement hysteresis behaviour of steel tubular members. Based on the general aspects of hysteretic behaviour and the traditional Marshall model, the modified Marshall model is developed to improve the simulation accuracy, whose control parameters are determined by batch parameter analysis results. For the applicability in multiple hysteresis loop process, the initial member curvature under compression-tension during hysteretic loop process is studied and the computation methods under compression and tension are given individually based on the finite element analysis results and theoretical derivation. On this foundation, the model control parameter correction and axial compression capacity redefined with large initial member curvature during hysteretic loop process are executed in the updated parametric hysteretic model proposed later in this paper. Finally, in addition to the comparison with the finite element results, the rationality and applicability of the proposed model are also verified by several experiments and the good agreement in loop curve trend and hysteretic energy consumption are found between the simulated and experimental results.

Hygrothermal environment effect on the critical buckling load of FGP microbeams with initial curvature integrated by CNT-reinforced skins considering the influence of thickness stretching

Abstract Due to the need for structures with refined properties to bear against different loading conditions, recently, carbon nanotubes (CNTs) have been used widely to reinforce them. The extremely high stiffness of CNTs makes them significant as one of the best reinforcements to improve the mechanical behaviors of structures. This work focuses on microbeam buckling response with an initial curvature that includes three layers. The mid-layer that is known as the core is constituted of functionally graded porous (FGP) materials and two CNT-reinforced composite skins are bonded to the core to integrate it. The whole structure is affected by the hygrothermal environment and springs and shear layers are put below it. For the first time, for such a structure, a refined shear deformation theory (RSDT) as a higher-order theory that considers thickness stretching effect in polar coordinates is used that presents more accurate results, especially for deeply curved beams. Modified couple stress theory (MCST) in combination with the virtual displacement principle is utilized to establish the governing equations. The obtained results demonstrate the significance of porosity percentage and CNTs’ addition to the skins on the critical nanotubes buckling load. Also, the different behaviors of the microstructure at various temperatures are analyzed and discussed in detail.