Rotational Degrees Research Articles

Development of Rail Camera for Bridge inspection with Attitude Control using Thrust of Rotors

A lot of concrete structures are deteriorating to dangerous levels throughout Japan. These concrete structures need to be inspected regularly to ensure they are safe enough to be used. According to national standards, a visual inspection of the bridge is required once every five years. In the visual inspection, the worker checks the bridge with their own eyes directly. So, it is necessary to set up scaffolding to access the bridge's underside for visual inspection. Alternatively, it is an essential aerial work platform. However, setting up of scaffolding and aerial work platforms is not economical in time and money. So, we developed an inspection device for the check of bridges called a Rail camera. This inspection device connects a rod and a rail and the connection has a rotational degree of freedom. Rotors are attached to the tip of the rod and it can be attitude controlled by thrust of rotors. So, half of the device's weight is lifted by the thrust of the rotors. And it can be taken with a camera mounted on an electric slider on the rail. The worker on the bridge can check the underside of the bridge safely by holding the rod with one hand and operating the rail camera with another hand. The rail camera developed had a rail length of 2 m and a weight of 2.5 kg. Magnesium was used for the rail and rod to reduce weight. Coaxial rotors were used to cancel the counter-torque caused by the rotation of the propeller. To verify the performance, a visual inspection was performed on the bridge. As a result, it was confirmed that the horizontal attitude was maintained by the rotor thrust.

Comment on: “Analytical solutions to the Schrödinger equation for a generalized Cornell potential and its applications to diatomic molecules and heavy mesons”

We analyze a recent calculation of the energy levels of some quantum-mechanical models derived from the so-called generalized Cornell potential. We argue that the authors obtained essentially the same spectrum for potentials with considerably different spectra. We show that the authors obtained negative eigenvalues in the case of a positive-definite potential. The reason is due to the approximation used in the solution of the Schrödinger equation. We point out that the omission of the sum over the rotational degrees of freedom in the canonical partition function leads to incomplete expressions for the thermodynamic functions.

A preliminary biomechanical assessment and user perceptions of a motorized lifter for patient transfer

ABSTRACT A “no-lift” policy in healthcare discourages manual patient lifting to reduce worker injuries. This study explores modifications to a floor lift (NEAR-1) to align with this policy. NEAR-1 features a shorter lower lifting arm and a redesigned sling, enabling patients to (a) transfer in a sitting position, unlike a floor lift’s semi-reclining position, and (b) feel more in control by removing the sling’s rotational degree of freedom and letting the patient’s feet rest on the lifter base. The device also reduced patient weight-bearing, compared to sit-to-stand lifts. Biomechanical analysis was done to map the risk to the nurses and capture the patient’s experience with the modified lift (NEAR-1). Thirteen subjects carried out patient transfer tasks using both the NEAR-1 and the manual transfer approach, and this comparison will provide the baseline data for future systematic reviews. From the results, NEAR-1 significantly reduced the L5-S1 compression, the mediolateral shear forces, and the anteroposterior shear forces, with the exception of the muscle activities in the lower back, the shoulder, and the biceps. Moreover, patients felt safer and more comfortable with the device. Overall, the NEAR-1 lifter presents a biomechanically beneficial and user-friendly option for patients with limited weight-bearing capability.

Pyrazolo-Pyrimidinones with Improved Solubility and Selective Inhibition of Adenylyl Cyclase Type 1 Activity for Treatment of Inflammatory Pain.

Adenylyl cyclase isoform 1 (AC1) is considered a promising target for treating inflammatory pain. Our group identified the pyrazolyl-pyrimidinone scaffold as potent and selective inhibitors of Ca2+/CaM-mediated AC1 activity; however, the molecules suffered from poor aqueous solubility. The current study presents a strategy to improve aqueous solubility of the scaffold by reduction of crystal packing energy and increasing rotational degrees of freedom within the molecule. Structure-activity and property relationship studies identified the second generation lead 7-47A (AC10142A) that demonstrated and AC1 IC50 value of 0.26 μM and aqueous solubility of 74 ± 7 μM. After in vitro ADME characterization, the scaffold advanced to in vivo pharmacokinetic evaluation, demonstrating adequate levels of exposure. Finally, 7-47A exhibited antiallodynic efficacy in a rat complete Freund's adjuvant model for inflammatory pain showing improvement over previous iterations of this scaffold. These results further validate AC1 inhibition as a viable therapeutic strategy for treating chronic and inflammatory pain.

Automated quality control analysis for American College of Radiology (ACR) digital mammography (DM) phantom images.

To develop and validate an automated software analysis method for mammography image quality assessment of the American College of Radiology (ACR) digital mammography (DM) phantom images. Twenty-seven DICOM images were acquired using Fuji mammography systems. All images were evaluated by three expert medical physicists using the Royal Australian and New Zealand College of Radiologists (RANZCR) mammography quality control guideline. To enhance the robustness and sensitivity assessment of our algorithm, an additional set of 12 images from a Hologic mammography system was included to test various phantom positional adjustments. The software automatically chose multiple regions of interest (ROIs) for analysis. A template matching method was primarily used for image analysis, followed by an additional method that locates and scores each target object (speck groups, fibers, and masses). The software performance shows a good to excellent agreement with the average scoring of observers (intraclass correlation coefficient [ICC] of 0.75, 0.79, 0.82 for speck groups, fibers, and masses, respectively). No significant differences were found in the scoring of target objects between human observers and the software. Both methods achieved scores meeting the pass criteria for speck groups and masses. Expert observers allocated lower scores to fiber objects, with diameters less than 0.61mm, when compared to the software. The software was able to accurately score objects when the phantom position changed by up to 25mm laterally, up to 5 degrees rotation, and overhanging the chest wall edge by up to 15mm. Automated software analysis is a feasible method that may help improve the consistency and reproducibility of mammography image quality assessment with reduced reliance on human interaction and processing time.

A Comparative Study on the Consistency of Ultrasound and X-Ray in Assessing Risser Sign.

Adolescent idiopathic scoliosis (AIS) is a 3-dimensional spinal deformity involving lateral curvature, sagittal plane imbalance, and vertebral rotation. In China, AIS affects over 3 million individuals, with 300,000 new cases annually. AIS impacts physical and psychological well-being, necessitating tailored treatment plans based on growth risk factors. This study evaluates the consistency of ultrasound and X-ray assessments of the Risser sign in AIS patients and explores correlations between iliac crest distance and pelvic rotation degree. This prospective study enrolled 80 patients diagnosed with AIS from June to September 2023 at Changzhou Sports Hospital. Eligible participants were aged 10-18 with a Cobb angle >10°. Ultrasonographic examinations were conducted by 3 experienced physicians using the VINNO V10 portable ultrasound system. The primary outcome was the Risser stage determined by X-ray and ultrasound, with secondary outcomes including thoracic and thoracic-lumbar segment rotation angles. Statistical analyses included kappa statistics, correlation analyses, and multiple regression. Among the 77 valid cases, 154 iliac wings were evaluated, with a high concordance rate of 77% between ultrasound and X-ray assessments. kappa values for left and right iliac crests were 0.723 and 0.808, respectively. Grouping Risser grades (0-1, 2-3, and 4-5) into 3 categories yielded kappa values of 0.93, 0.96, and 0.93, indicating high consistency. Significant correlations were found between iliac crest distances and rotation angles (left iliac crest distance and left thoracic rotation angle, r = 0.56, P < .001; right iliac crest distance and right thoracic-lumbar rotation angle, r = 0.69, P < .001; right iliac crest distance and right thoracic rotation angle, r = 0.39, P < .01). Ultrasound is a reliable, radiation-free alternative to X-ray for assessing the Risser sign in AIS patients. Despite observed inconsistencies in intermediate Risser grades, ultrasound's ability to reduce radiation exposure and provide consistent results makes it a valuable tool in clinical practice. Further research is needed to optimize ultrasound techniques and explore its potential for early detection and intervention in scoliosis management.

The benefit of choice on task performance: Reduced difficulty effects in free-choice versus forced-choice tasks.

We investigated how self-determined (free) versus imposed (forced) choices influence task performance. To this end, we examined how changes in perceptual and central decision-processing difficulties affect task performance in an environment where free-choice and forced-choice tasks were intermixed. In Experiments 1 (N = 43) and 2 (N = 42), perceptual processing difficulty was varied by altering colored dot proportions (easy vs. hard color discrimination task). In Experiment 3 (N = 58), decision-processing difficulty was adjusted by changing the rotation degree of letters (easy vs. hard letter rotation task). Across all experiments, both free-choice and forced-choice performance were more impaired with harder stimuli, but this effect was generally less pronounced in freely chosen tasks. Specifically, this was evident from significant interactions between processing mode (free vs. forced) and difficulty (easy vs. hard) in the mean reaction times (RTs) for the tasks with the difficulty manipulation. Thus, processing in free-choice tasks is generally less affected by environmental changes (i.e., variation in information difficulties). We discuss how the benefit of self-determined choices over imposed choices can be explained by motivational and performance-optimization accounts, while also considering the finding that participants adjusted their task choices toward tasks with easier stimuli (i.e., significant main effect of task difficulty on choosing the task with the difficulty manipulation). Specifically, we discuss how having control over task choices might lead to more stable information processing and allow people to choose more difficult tasks when this increased difficulty has a relatively small impact on their performance.

Degraded oculomotor function and its implications on balance in pediatric strabismus

BackgroundChildren with visual impairment often exhibit poor postural control. However, the effects of strabismus on oculomotor system components and its impact on balance in children are not yet fully understood. This study aims to determine the potential effects of oculomotor functions on balance skills in children with strabismus.MethodsA total of 30 children aged between 6 and 10 years participated in this study. Fifteen children diagnosed with strabismus were included in the strabismus group (8.07 ± 1.33 years), and 15 healthy children without any vision problems were included in the control group (8.03 ± 1.49 years). All children underwent a comprehensive hearing evaluation, bedside neurological and balance examinations, the Pediatric Balance Scale (PBS) assessment to assess balance function, and Videonystagmography (VNG) tests to measure oculomotor function.ResultsIn the saccade test, no significant differences were found between the groups in terms of latency, accuracy, and speed (p > 0.05). The strabismus group showed significantly lower pursuit test gains (except the left eye at 0.4 Hz) (p < 0.05) and significantly higher asymmetries (except the right eye at 0.4 Hz) (p < 0.05). No significant difference was observed between the groups in optokinetic test gains (p > 0.05). The strabismus group had significantly lower scores on the 360-degree rotation task (10th item) (p = 0.027) and total PBS scores (p = 0.029). Correlation analysis revealed statistically significant negative correlations between strabismus angle and optokinetic test gains, pursuit test gains, and PBS total scores, with varying correlation strengths (p < 0.05 and − 0.639 < r < − 0.338).ConclusionsStrabismus adversely affects the optokinetic and pursuit systems, as well as balance in children. Furthermore, an increase in the strabismus angle is associated with greater adverse effects on these functions. The lower scores obtained in the PBS scores of the strabismus group indicate that strabismus may negatively affect balance skills in activities of daily living. Early intervention and targeted therapies should be considered to mitigate these effects and support the development of balance skills in children with strabismus.

Rotational stability of plate-haptic toric intraocular lenses implantation with a capsular tension ring: a prospective randomized paired-eye study.

To compare the rotational stability and visual outcomes of plate-haptic toric intraocular lenses (IOLs) with and without a capsular tension ring (CTR) in paired eyes. Eye and Ears, Nose, and Throat Hospital of Fudan University, Shanghai, China. Prospective, randomized, paired-eye study. Patients with bilateral cataracts and coexisting regular corneal astigmatism were enrolled. The two eyes of each patient were randomly assigned to the CTR or non-CTR (NCTR) group. Both eyes of each patient were subjected to phacoemulsification and toric IOL implantation. CTRs were implanted into the eyes of the CTR group. All patients were followed-up for 12 months; the uncorrected distance visual acuity (UDVA), residual astigmatism (RAS), and rotational degree of the toric IOL were recorded. In total, 186 eyes of 93 patients were eligible for analysis. At each visit, UDVA improved significantly after surgery in all eyes (p < 0.001). The mean rotational degree and RAS were significantly smaller in the CTR group at the 2-week visit (p < 0.05). The toric IOLs achieved rotational stability at 1 week postoperatively in the CTR group while at 2 weeks postoperatively in the NCTR group. In the subgroup analyses, CTR co-implantation significantly reduced the 2-week IOL rotation in eyes meeting specific ocular measurements. CTR co-implantation could increase the rotational stability of plate-haptic toric IOLs, by reducing the amount of the IOL rotation in the early postoperative period and accelerating the stabilization of IOLs in the capsular bag.

Research on the ultra-low temperature tensile deformation mechanism of Al-Mg-Si alloys in different heat treatment states

The susceptibility of Al-Mg-Si alloy to cracking during room temperature large plastic deformation poses a significant obstacle to its widespread application. Cryogenic temperature forming of aluminum alloys has emerged as a prominent research topic. However, the precise mechanisms underlying the enhancement of aluminum alloy plasticity in different states remain elusive. In order to elucidate this matter, a series of uniaxial tensile experiments were conducted on Al-Mg-Si alloy featuring diverse initial states, under varying temperature conditions. The results show that when the deformation temperature is reduced from 25℃ to -196℃, the tensile strength and elongation of the wrought material are increased by 48MPa and 5.42%, and the tensile strength and elongation of the annealed material are increased by 118MPa and 5.65%. In contrast, while the T4 state sample exhibited a significant improvement in tensile strength (103MPa), no substantial enhancement in elongation was observed. This disparity can be primarily attributed to the absence of second-phase precipitation in the as-forged and annealed states. As the temperature decreased, the critical shear stress increased, resulting in increased resistance to deformation. Consequently, an increased degree of lattice rotation and activation of dislocations in various slip systems ensued, thereby improving the deformation uniformity. The formation of initial microvoids predominantly occurred close to grain boundaries. Therefore, compared with room temperature deformation, low temperature deformation caused by the accumulation of dislocations and hole sprouting concentrated at a single location was less likely. As a result, the dislocation distribution was more uniform and fracture was less likely to occur. Conversely, in the T4 state, the aging process resulted in the precipitation of a substantial amount of the soluble second phase (Mg5Si6). Consequently, microvoid nucleation transpired at the phase boundaries, leading to an elevated tensile strength. However, because of the increased dislocation hindrance when the deformation temperature was lowered, no significant enhancement in plasticity was observed.

The effect of femoral strapping on hip internal rotation and pain response in females with patellofemoral pain

BackgroundHip internal rotation has been reported to affect patellofemoral joint mechanics and contribute to patellofemoral pain (PFP). The SERF (Stability through External Rotation of the Femur) strap was designed to provide hip stability by pulling the thigh into external rotation during weight-bearing activities. Research questionWhat are the effects of the SERF strap on hip internal rotation and pain response in females with PFP who present with hip internal rotation during weight-bearing activities? MethodsNineteen females between the ages of 18 and 45 with a diagnosis of PFP participated. Lower extremity kinematics were obtained during three tasks (drop-jump, unilateral step-down, over-ground running) under strap and no-strap conditions. A 10-cm visual analog scale (VAS) was used to assess pain response during each task and strap condition. Participants who exhibited at least 5 degrees of hip internal rotation during at least one of the 3 tasks were included in the final analysis. Peak hip internal rotation and mean VAS score were compared separately between strap conditions across tasks using 2 ×3 (strap condition x task) repeated-measures ANOVAs. ResultsEighteen of the 19 females with PFP met the criteria for the presence of hip internal rotation. There was a significant reduction in peak hip internal rotation across tasks when wearing the SERF strap (mean ± sd = 7.4 ± 2.3, p<0.001). Additionally, the change in mean VAS pain score was significantly lower across tasks when wearing the SERF strap (1.0 ± 1.0, p=0.03). SignificanceThe SERF strap was effective in reducing hip internal rotation and PFP during dynamic weight-bearing activities in symptomatic females. The SERF strap may be a useful treatment adjunct for persons with PFP who present with poor transverse plane control of the hip.

Magnetically Tunable Electric Dipolar Interactions of Ultracold Polar Molecules in the Quantum Ergodic Regime.

By leveraging the hyperfine interaction between the rotational and nuclear spin degrees of freedom, we demonstrate extensive magnetic control over the electric dipole moments, electric dipolar interactions, and ac Stark shifts of ground-state alkali-dimer molecules such as KRb(X^{1}Σ^{+}). The control is enabled by narrow avoided crossings and the highly ergodic character of molecular eigenstates at low magnetic fields, offering a general and robust way of continuously tuning the intermolecular electric dipolar interaction for applications in quantum simulation, quantum sensing, and dipolar spinor physics.

Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration.

The deep unfolding approach has attracted significant attention in computer vision tasks, which well connects conventional image processing modeling manners with more recent deep learning techniques. Specifically, by establishing a direct correspondence between algorithm operators at each implementation step and network modules within each layer, one can rationally construct an almost "white box" network architecture with high interpretability. In this architecture, only the predefined component of the proximal operator, known as a proximal network, needs manual configuration, enabling the network to automatically extract intrinsic image priors in a data-driven manner. In current deep unfolding methods, such a proximal network is generally designed as a CNN architecture, whose necessity has been proven by a recent theory. That is, CNN structure substantially delivers the translational symmetry image prior, which is the most universally possessed structural prior across various types of images. However, standard CNN-based proximal networks have essential limitations in capturing the rotation symmetry prior, another universal structural prior underlying general images. This leaves a large room for further performance improvement in deep unfolding approaches. To address this issue, this study makes efforts to suggest a high-accuracy rotation equivariant proximal network that effectively embeds rotation symmetry priors into the deep unfolding framework. Especially, we deduce, for the first time, the theoretical equivariant error for such a designed proximal network with arbitrary layers under arbitrary rotation degrees. This analysis should be the most refined theoretical conclusion for such error evaluation to date and is also indispensable for supporting the rationale behind such networks with intrinsic interpretability requirements. Through experimental validation on different vision tasks, including blind image super-resolution, medical image reconstruction, and image de-raining, the proposed method is validated to be capable of directly replacing the proximal network in current deep unfolding architecture and readily enhancing their state-of-the-art performance. This indicates its potential usability in general vision tasks.

Study of chemiluminescence of methane–air flame stabilized on a flat porous burner

In this work, the spatial distribution and spectral characteristics of the chemiluminescence of chemically excited species, OH∗ and CH∗, are experimentally and numerically studied by using a stationary premixed methane–air flame stabilized on the surface of a flat porous burner for various equivalence ratio and normal pressure. Numerical simulations are carried out using detailed reaction mechanisms, and the experimental study includes high-resolution spatial and spectral optical measurements. Despite the data reported in the literature, it is found that (i) the rotational degrees of freedom of OH∗ and CH∗ are not in thermal equilibrium with the surrounding gas and therefore cannot be used to measure flame temperature; (ii) there is no direct correlation between the heat release rate and the distribution of OH∗ and CH∗; (iii) the detailed reaction mechanisms not only quantitatively, and also qualitatively differ in description of the OH∗ and CH∗ concentrations. Since the chemically excited species are well localized in a direction normal to the flame surface, they are demonstrated to be a very accurate markers of flame location. The shape of the combustion front can be reconstructed and resolved up to the accuracy of tens of microns, which is very important for estimation of blow-off critical parameters and measurement of the laminar burning velocity.Novelty and significance statementCurrently, there is a growing interest in the development of sensors for combustion control systems, including active control and suppression of instabilities, in combustion chambers of various devices and engines based on chemiluminescence of excited reaction species. The possibility of non-invasive determination of parameters such as flame temperature, stoichiometry, heat release rate location, etc. using this technique is discussed. We have found that most of these parameters cannot be estimated either due to fundamental limitations or insufficient knowledge of the reaction kinetics involved in the production of these species. Nevertheless, since OH* and CH* are well localized in the direction normal to the flame surface, they can be used as very accurate markers of flame shape and position, allowing us to reconstruct the flame surface to within tens of microns resolution, which is very important for estimating blow-off critical parameters and measuring laminar burning velocity.

Machine-learned coarse-grained potentials for particles with anisotropic shapes and interactions

Computational investigations of biological and soft-matter systems governed by strongly anisotropic interactions typically require resource-demanding methods such as atomistic simulations. However, these techniques frequently prove to be prohibitively expensive for accessing the long-time and large-length scales inherent to such systems. Conversely, coarse-grained models offer a computationally efficient alternative. Nonetheless, models of this type have seldom been developed to accurately represent anisotropic or directional interactions. In this work, we introduce a straightforward bottom-up, data-driven approach for constructing single-site coarse-grained potentials suitable for particles with arbitrary shapes and highly directional interactions. Our method for constructing these coarse-grained potentials relies on particle-centered descriptors of local structure that effectively encode dependencies on rotational degrees of freedom in the interactions. By using these descriptors as regressors in a linear model and employing a simple feature selection scheme, we construct single-site coarse-grained potentials for particles with anisotropic interactions, including surface-patterned particles and colloidal superballs in the presence of non-adsorbing polymers. We validate the efficacy of our models by accurately capturing the intricacies of the potential-energy surfaces from the underlying fine-grained models. Additionally, we demonstrate that this simple approach can accurately represent the contact function (shape) of non-spherical particles, which may be leveraged to construct continuous potentials suitable for large-scale simulations.

Rotational deformation twins in a HfNbTaTiZr refractory high entropy alloy

Results of the analysis of deformation twins formed in a HfNbTaTiZr refractory high entropy alloy during compression deformation at 20 °C – 600 °C are reported. All studied twins were formed by rotation of the matrix crystal lattice around a 〈110〉 pole and have the common reciprocal twinning plane K2 = {001} and reciprocal twinning direction η2 = <11¯0>. At the same time, the twinning plane K1 and direction η1 depend on the degree of rotation of K2 and η2 around the common 〈110〉 pole. The following rotational twinning modes have been identified in HfNbTaTiZr: {11¯4}<22¯1¯> (38.94° rotation), {11¯5}<55¯2¯> (31.58°), {11¯6}<33¯1¯> (26.54°), {11¯7}<77¯2¯> (22.84°), and {11¯8}<44¯1¯> (20.04°). A rotational mechanism of twinning, with the rotation axis 〈011〉 or 〈001〉, is proposed as an alternative to the commonly accepted shear mechanism.

Rotational properties of two interacting cold polar molecules: Linear, symmetric, and asymmetric tops

We examine the potential-energy curves and polarization of the dipole moments of two static polar molecules under the influence of an external dc electric field and their anisotropic dipole-dipole interaction. We model the molecules as quantum rigid rotors to take their rotational degrees of freedom into account and consider a selection of linear, symmetric, and asymmetric top molecules. We provide a comprehensive examination of the energy curves and polarization of the dipoles for varying intermolecular separation and direction of the electric field and find that the properties of the molecules depend strongly on the field's direction at short separations, showing the importance of accounting for molecular rotation. The latter provides insight into the possible effects of accounting for rotational degrees of freedom in molecular dipolar gases. Published by the American Physical Society 2024

Micro computed tomography analysis of barley during the first 24 hours of germination

BackgroundGrains make up a large proportion of both human and animal diets. With threats to food production, such as climate change, growing sustainable and successful crops is essential to food security in the future. Germination is one of the most important stages in a plant’s lifecycle and is key to the success of the resulting plant as the grain undergoes morphological changes and the development of specific organs. Micro-computed tomography is a non-destructive imaging technique based on the differing x-ray attenuations of materials which we have applied for the accurate analysis of grain morphology during the germination phase.ResultsMicro Computed Tomography conditions and parameters were tested to establish an optimal protocol for the 3-dimensional analysis of barley grains. When comparing optimal scanning conditions, it was established that no filter, 0.4 degrees rotation step, 5 average frames, and 2016 × 1344 camera binning is optimal for imaging germinating grains. It was determined that the optimal protocol for scanning during the germination timeline was to scan individual grains at 0 h after imbibition (HAI) and then the same grain again at set time points (1, 3, 6, 24 HAI) to avoid any negative effects from X-ray radiation or disruption to growing conditions.ConclusionHere we sought to develop a method for the accurate analysis of grain morphology without the negative effects of possible radiation exposure. Several factors have been considered, such as the scanning conditions, reconstruction, and possible effects of X-ray radiation on the growth rate of the grains. The parameters chosen in this study give effective and reliable results for the 3-dimensional analysis of macro structures within barley grains while causing minimal disruption to grain development.

An efficient isogeometric buckling optimization framework for multi-patch laminated shells: Leveraging 3D solid elements, lamination parameters and penalty method

Buckling is a common failure mode of laminated shell structures during service, and isogeometric analysis methods are highly suitable for the buckling analysis due to their accurate geometric modeling capability and high-order continuity. However, the isogeometric buckling analysis for a multi-patch structure and its optimal design still face challenges in computational efficiency. To address this issue, this paper proposes an integrated framework for the buckling optimization of multi-patch laminated shells, which leverages 3D solid elements, lamination parameters, and the penalty coupling method. Solid-shell elements have advantages in shell analysis due to their simplicity, absence of rotational degrees of freedom, and adaptive layering in the thickness direction. Lamination parameters simplify the optimization of fiber orientations in laminated shells by condensing the design variable space and improving the convexity of the optimization problem. The penalty method can handle the coupling in multiple patches at a relatively low cost. Nevertheless, lamination parameters are rarely applied to the case of solid-shell elements. In addition, despite using lamination parameters, the number of design variables for multi-patch structures remains significantly large. To tackle these issues, this study derives the solid-shell formulation in lamination parameters and the sensitivity analysis formulae in the reverse mode. Experiment validation is conducted to assess the accuracy of the proposed method based on lamination parameters with solid elements, the feasibility of the multi-patch optimization model, and the computational efficiency of optimization sensitivity based on the reverse mode compared to the forward counterpart common in the literature.

Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model

For nonlinear Cosserat elasticity, we consider multiscale methods in this paper. In particular, we explore the generalized multiscale finite element method (GMsFEM) to solve an isotropic Cosserat problem with strain-limiting property (ensuring bounded linearized strains even under high stresses). Such strain-limiting Cosserat model can find potential applications in solids and biological fibers. However, Cosserat media with naturally rotational degrees of freedom, nonlinear constitutive relations, high contrast, and heterogeneities may produce challenging multiscale characteristics in the solution, and upscaling by multiscale methods is necessary. Therefore, we utilize the offline and residual-based online (adaptive or uniform) GMsFEM in this context while handling the nonlinearity by Picard iteration. Through various two-dimensional experiments (for perforated, composite, and stochastically heterogeneous media with small and big strain-limiting parameters), our numerical results show the approaches' convergence, efficiency, and robustness. In addition, these results demonstrate that such approaches provide good accuracy, the online GMsFEM gives more accurate solutions than the offline one, and the online adaptive strategy has similar accuracy to the uniform one but with fewer degrees of freedom.