This study propounds a sustainable alternative to petroleum-based polyurethane (PU) foams aiming to curtail this nonrenewable resource's continued and uncontrolled use. Coconut fatty acid distillate (CFAD) and crude glycerol (CG), both wastes from vegetable oil processes, were utilized for bio-based polyol production for rigid PU foam application. The raw materials were subjected to catalyzed glycerolysis with alkaline-alcohol neutralization and bleaching. The resulting polyol possessed properties suitable for rigid foam application with an average OH number of 215 mg KOH/g, acid number of 7.2983 mg KOH/g, and Gardner color value of 18. The polyol was used to prepare rigid PU foam, and its properties were determined using FTIR, TGA/DTA, and UTM. Additionally, the cell foam morphology was investigated by scanning electron microscope (SEM) in which most of its structure revealed an open-celled network and quantified at 92.71% open cell content using pycnometric testing. The PU foam thermal and mechanical analysis results showed an average compressive strength of 70.59 kPa, thermal conductivity of 46.50 mWm-1K-1, and density of 32.79 kgm-3. These properties showed its applicability as thermal insulating foam, thus, demonstrating the potential use of CFAD and CG in commercial polyol and PU foam production.

Planar differential systems whose angular velocity is constant are called rigid differential systems. We characterize the existence and non-existence of limit cycles, and the finite and infinite singularities of the rigid polynomial differential systems with homogeneous nonlinearities of arbitrary degree in the Poincaré disc. Moreover, we classify the phase portraits in the Poincaré disc of the rigid polynomial differential systems of degree two, and of one class of rigid polynomial differential systems with cubic homogeneous nonlinearitie that can exhibit one limit cycle.

Finding a solution for Euler's equations is a classic mechanics problem. This study revisits the problem with numerical approaches. For ease of teaching and research, a Maple code comprising 2 lines is written to find a numerical solution for the problem. The study's results are validated by comparing these with previous studies. Our results confirm the correctness of the principle of maximum moment of inertia of the rotating body, which is verified by thermodynamics. As an essential part of this study, the Maple code is provided.

It is shown that for any integers k≥2, q≥2k and N≥k+q+2 there exists a real solvable Lie algebra of rank one with a maximal torus of derivations t possessing the eigenvalue spectrum spec(t)=1,2,⋯,k,q,q+1⋯,N and a nilradical of nilpotence index N−k and characteristic sequence (N−k,1k).

As the coproduct of steelmaking, steelmaking slag, volumetrically expansive-prone without treatment, has been satisfactorily used as an aggregate base course material in highway construction. Although numerous technical reports and papers have revealed that steel slag aggreged using in rigid matrixes, the end product, paving block, non-structural concrete, for example, possesses superb strength and durability properties, the application of steel slag aggregate as a concrete aggregate is currently prohibited in highway construction. Naturally, researchers explore the practicality of use of steel slag, how to connect the laboratory experiment results to the end-product behavior, and further convert the research results into real construction? For all nontraditional or secondary materials utilization, the procedure of laboratory material examination, lab and field trial test are critical. To generalize the utilization, usability criteria establishment is necessary. This paper tries to use step-by-step method and plain language to explain how the volumetrically expansion can be simulated in lab testing apparatus, and based on the model, the mathematical deduction can result in a numerical usability criterion for steel slag use as a coarse aggregate in concrete (a rigid material). Therefore the paper is composed four main parts, laboratory test methods to examine the expansion force resulted from steel slag; converting the measured expansion force in a given volume of mass aggregate to the expansion (body) force of a single particle; modeling of slag and end material disruption; and a usability criterion from numerical deduction for the use of expansive-prone coarse slag in concrete or other rigid matrices. The paper provides the solutions to answer the above questions. Through the mathematical and mechanical modeling, provides the potential criteria that could result in specifications and guidance establishment for broad volumetric expansive-prone slags.

A method of measuring the absolute pose parameters of a moving rigid body using a monocular camera is proposed, aiming at addressing calibration difficulties and inconsistencies of repeated measurements of the rigid-body pose for a camera having a varying focal length. The proposed method does not require calibration beforehand. Using more than six non-coplanar control points symmetrically arranged in the rigid-body and world coordinate systems, the matrices of rotation and translation between the camera and two coordinate systems are obtained and the absolute pose of the rigid body measured. In this paper, formulas of the absolute pose measurement of a moving rigid body are deduced systematically and the complete implementation is presented. Position and attitude measurement experiments carried out on a three-axis precision turntable show that the average absolute error in the attitude angle of a moving rigid body measured by an uncalibrated camera at different positions changes by no more than 0.2 degrees. Analysis of the three-dimensional coordinate errors of the centroid of a moving rigid body shows little deviation in measurements made at three camera positions, with the maximum deviation of the average absolute error being 0.53 cm and the maximum deviation of the standard deviation being 0.66 cm. The proposed method can measure the absolute pose of a rigid body and is insensitive to the position of the camera in the measurement process. This work thus provides guidance for the repeated measurement of the absolute pose of a moving rigid body using a monocular camera.

Due to the fact that irrigation networks are water and energy-hungry and that both resources are scarce, many strategies have been developed to reduce this consumption. Otherwise, solar energy sources have become a green alternative with lower energy costs and, as a consequence, lower environmental impacts. In this work, it is proposed a new methodology to select the scheduled program for irrigation which minimizes the number of photovoltaic solar panels to be installed and which better fits energy consumption (calculated for discrete potential combinations; using a programming software to assist) to available energy obtained by panels without any power conditioning unit. So, the irrigation hours available to satisfy the water demands are limited by sunlight, the schedule type of irrigation has to be rigid (rotation predetermined) and the pressure at any node has to be above the minimum pressure required by standards. A real case study has been performed.

This paper presents a novel normative framework for assessing granular base materials in rigid pavements, incorporating evaluations of California Bearing Ratio (CBR) alongside hydraulic conductivity tests. A critical component of this research adheres to Federal Highway Administration (FHWA) standards, which specify a permeability coefficient range of 0.05 to 0.20 cm/sec. Our investigations indicate that increased compaction energy inversely affects permeability, highlighting a sophisticated interplay between compaction dynamics and hydraulic characteristics. The study further elucidates that CBR values are profoundly impacted by the content of coarse-grained soil, advocating for a tailored approach to base layer assessment. Multivariable CBR analysis facilitated the identification of an optimal water content, underscoring that maintaining a minimum 80% CBR—while minimizing water content—can mitigate fatigue effects and enhance structural performance under heightened energy conditions. This research proposes bespoke, scientifically validated standards that integrate local geotechnical nuances, aimed at refining material selection processes and extending the durability of pavement infrastructures through foundational yet meticulous geotechnical evaluations.

Aiming at the problem that soft robots are challenging to take into account both flexibility and bearing capacity, Using the software Pneu-Net driver as the deformation mode, magnetorheological fluid material phase transformation to achieve variable stiffness, A pneumatic modular soft joint structure with dynamically adjustable deformation and stiffness in all directions is proposed. In this paper, mathematical models of deformation and variable stiffness are established. The correspondence between gas pressure and deformation and applied current and joint stiffness is obtained. The finite element analysis method was used to simulate the deformation characteristics and variable stiffness characteristics of modular joints based on the Yeoh model. Finally, the theoretical and simulation results are verified by deformation and variable stiffness tests. It is proved that the modular joint has good rigid-flexible coupling characteristics.

Cavitation bubbles are commonly existing in shipbuilding engineering, ocean engineering, mechanical engineering, chemical industry, and aerospace. Asymmetric deformation of bubble occurs near the boundary, and the non-spherical cavitation bubbles have strong destructive effects, inducing high amplitude loading at the nearby boundary. The purpose of this paper is to investigate the laser-induced of cavitation bubble, non-spherical collapse behavior near the boundary. In this study, experimental data such as bubble pulsation process and bubble surface velocity distribution were obtained by high-speed camera technique and full-field velocity calculation. The results show that the bubble appeared non-spherical collapse shapes, near different boundaries, with near-hemispherical, near-ellipsoidal, near-cone and near-pea shapes, and the bubble surface velocity distribution is not uniform. When bubble near the free surface or rigid boundary, the smaller the stand-off r is, the more obvious the repulsive effect of the free surface and the attractive effect of the rigid boundary are. As the stand-off r decreases, the larger the Bjerknes force and the bubble surface velocity difference, the more pronounced the non-spherical shape.

The engagement of the arresting hook with the arresting cable is a critical maneuver that is essential to the safe operation of aircraft landing on aircraft carrier. A comprehensive understanding of the engagement process dynamics is necessary to optimize landing performance and ensure the safety and efficiency of carrier operations. In this paper, an efficient and accurate simulation and analysis method is presented for studying the arresting hook engaging arresting cable process. The Finite Element Method and Multibody Dynamics (FEM-MBD) approach is employed. By establishing a rigid-flexible coupling model encompassing the aircraft frame, arresting hook, carrier deck and arresting gear system, the dynamic model for the engagement process is obtained. The model incorporates multiple coordinate systems to effectively capture the relative motion between the rigid and flexible components, enabling a thorough understanding of the dynamics characteristics. The analysis conducted in this paper takes into account various factors, including the material properties of the components, the characteristics of the arresting gear system, and the state of the aircraft during the engagement process. The analysis method is verified by comparing the simulation results with experiments of arresting hook rebound obtained from reference. Finally, simulations are performed to analyze the engagement process under different touchdown points and rolling angle of aircraft. The simulation results provide valuable insights into the distribution of stresses during the arresting hook and cable engagement, the center of gravity variations, as well as the response of the tire touch and rollover cable under specific scenarios. The proposed rigid-flexible coupling arresting dynamics model in this paper enables effective analysis of the dynamic behavior during arresting hook engaging arresting cable. The results obtained from this analysis offer valuable insights into the performance of the engagement process, which can be used to improve the design of carrier-based aircraft and techniques for carrier landing.

Cardiovascular-related diseases are one of the leading causes of death worldwide. An understanding of heart movement based on images plays a vital role in assisting the procedure in the postoperative and postoperative processes. In particular, if the shape information can be provided in real-time using the electrocardiogram(ECG) signal using this information, the heart’s movement information can be used for cardiovascular analysis and imaging guides during surgery. In this paper, we propose creating a 3D+t cardiac coronary artery model that is rendered in real-time according to the ECG signal. Hierarchical cage-based deformation modeling is used to generate mesh deformation used during the procedure according to the ECG signal. We match the blood vessel’s lumen obtained from the ECG-gated 3D+t CT angiography taken at the multiple cardiac phases to derive the optimal deformation. Splines for 3D deformation control points were used to continuously represent the obtained deformation at the multi-view according to the ECG signal. To verify the proposed method, we compared the manually segmented lumen and results of the proposed method for eight patients. The average distance and dice coefficient between the two models was 0.543mm and 0.735, respectively. The required time for registration of the 3D coronary artery model is 23.53 seconds/model. rendering speed to derive the model according to the ECG signal after generating the 3D+t model is faster than 120 FPS.

Remote sensing image registration plays an important role in military and civilian fields, such as natural disaster damage assessment, military damage assessment and ground targets identification, etc. However, due to the ground relief variations and imaging viewpoint changes, non-rigid geometric distortion occurs between remote sensing images with different viewpoint, which further increases the difficulty of remote sensing image registration. To address the problem, we propose a multi-viewpoint remote sensing image registration method which contains the following contributions. (i) A multiple features based finite mixture model is constructed for dealing with different types of image features. (ii) Three features are combined and substituted into the mixture model to form a feature complementation, i.e., the Euclidean distance and shape context are used to measure the similarity of geometric structure, and the SIFT (scale-invariant feature transform) distance which is endowed with the intensity information is used to measure the scale space extrema. (iii) To prevent the ill-posed problem, a geometric constraint term is introduced into the L2E-based energy function for better behaving the non-rigid transformation. We evaluated the performances of the proposed method by three series of remote sensing images obtained from the unmanned aerial vehicle (UAV) and Google Earth, and compared with five state-of-the-art methods where our method shows the best alignments in most cases.

With the galaxy J101652.52 as a model galaxy, this paper studied on the temporal duration of optically observed spiral patterns in disc galaxies is based on the finite reservoir of hydrogen available without replenishment following the initial formation of these well-isolated galaxies. The galaxy J101652.52 exhibits a grand design spiral pattern of two wide open spiral arms with perfect central symmetry, has only rear side trail effect, which clearly indicates that there is no corotation circle, therefore, the Density wave theory proposed for the spiral arm formation may not be applicable in this galaxy. The results reveal a gradual decline in observable spiral arms regardless of any spiral arm formation mechanism. This reduction occurs after half-loop rotation (as defined in the paper) as hydrogen reserves deplete, hindering new star formation. Ultimately, spiral patterns may possibly become optically invisible at normal conditions after a full-loop rotation (as defined in the paper) with hydrogen depletion, even if the formation mechanism remains active. The spiral galaxies with spiral arms decoupled from galactic bars or having soft spiral structures shall have similar results as long as that the spiral pattern rotation speed is significant different from the galactic matter rotation speed. Most of observed spiral galaxies have soft spiral structures, their spiral patterns dynamically change constantly. The results of this study support the idea of short-lived spiral patterns compared to the lifespan of the spiral galaxies. The spiral arm formation may occur once like the onetime firework show in a galaxy’s life based on the limited availability of hydrogens. A concise, universally applicable mechanism for spiral arm formation across various galaxies should exist which provides a single mathematical formula to describe the broad range of morphologies of the spiral arms with few adjustable parameters. Some exceptions may be explained within this framework. Furthermore, the observed data on spiral pattern and galactic bar rotation speeds in the Milky Way require rigorous verification, particularly concerning the winding problem.

The attitude dynamics and orbit dynamics of large rigid space structures are coupled with each other under gravity gradient, which may affect the stability of the large rigid space structures. In this paper, the gravity gradient stability of a large rigid space structure is studied under both small and large disturbances. Based on the rigid body dynamics and orbit dynamics, an accurate dynamic model without any linearization of the large rigid space structure is established via the natural coordinate formulation (NCF), which is able to describe the large overall motions of the structures. By using the generalized-α algorithm, the gravity gradient stability of the large rigid space structure is simulated and analyzed via various examples, including the influence of large disturbance angles, the positions at the stabilization and unstabilization regions. Finally, the relationship between spinning stability and gravity gradient stability is also investigated via a large spinning space structure.

Understanding the binding behavior and conformational dynamics of intrinsically disordered proteins (IDPs) is crucial for unraveling their regulatory roles in biological processes. However, their lack of stable 3D structures poses challenges for analysis. To address this, we propose an algorithm that explores IDP binding behavior with protein complexes by extracting topological and geometric features from the protein surface model. Our algorithm identifies a geometrically favorable binding pose for the IDP and plans a feasible trajectory to evaluate its transition to the docking position. We focus on IDPs from Homo sapiens and Mus-musculus, investigating their interaction with the Plasmodium Falciparum (PF) pathogen associated with malaria-related deaths. We compare our algorithm with HawkDock and HDOCK docking tools for quantitative (computation time) and qualitative (binding affinity) measures. Our results indicate that our method outperforms the compared methods in computation performance and binding affinity of experimental conformations.

Rigid-hulled inflatable boats are extremely practical and popular nowadays. They offer a effective conciliation among usability and costs. Their stable and seaworthy behaviour is guaranteed by performing hydroplaning hulls coupled with unsinkable inflated tubes. At the same time, their design is often based on tradition and preconceptions. Rarely, the design assumptions are validated by the reality or, even, by deeper investigations. In this article, both numerical methods and experimental mechanics techniques are proposed as an essential way for supporting the designers in their decisive tasks. Three different situations are detailed where a numerical or an experimental approach shows its benefit inside the engineering design process: firstly permitting to investigate the behaviour of materials driving the fiberglass selection; then measuring the levels of stress and strain in the hull during sailing; finally, using all available information as a base for developing numerical models of the hull slamming in waves. Even if the discussion is focused on a rigid inflatable boat, large part of its considerations is relevant beyond this special case.

Vegetation has a significant influence on velocity distribution and turbulent energy in a confluence channel. A laboratory measurement with ADV was used to investigate the flow through a Y-shaped confluence channel partially covered with rigid vegetation on its inner bank. In this study, the flow velocities in cases with and without vegetation were measured by the ADV in a Y-shaped confluence channel. The results clearly show that the existence of non-submerged rigid plants has changed the internal flow structure, that the velocity in the non-vegetated area is greater than in the vegetated area, and that there is a large exchange of mass and momentum between the vegetated and non-vegetated areas. The velocity on both sides is significantly reduced when vegetation is present. In the vicinity of tributaries, due to the presence of vegetation, the high-velocity area moved rapidly to the middle of the non-vegetated area, and the secondary flow phenomenon disappeared. In the mainstream, when vegetation was present, circulation disappeared, and the degree of lateral mixing decreased. The presence of vegetation caused a great change in the internal flow structure and made the flow in non-vegetated areas more intense.

This paper proposes a lightweight joint with bamboo culm cross connection, which is constructed by screwing one side of the screw into the other side of the wooden plug, its simple construction makes it easy to manufacture and cost-effective. This form connects adjacent bamboo culms to form corner joints, and bolt connects adjacent bamboo culm frames to form edge joints, to explore the mechanical properties of the combination joints formed by corner joints and edge joints, by combining experiments and numerical simulations, the method discovered and explained the relationship and mechanism between the number and position of bolts and the stiffness of edge joints. A calculation model for frame-unit bamboo culm members considering semi-stiffness of joints is proposed, and the conversion equations between linear stiffness of corner and edge joint and their rotational stiffnesses are derived. By establishing the series and parallel relationship between the corner and edge joints in the assembled members, a generalized relational equation between the total stiffness of the assembled joint and the stiffness of the corner and edge joints is derived. A numerical simulation method for frame-unit bamboo culm members with semi-rigid joints is proposed, which can obtain the stiffness calculation formula of edge joints and the average rotational stiffness value of semi-rigid corner joints. A finite element analysis method based on semi-rigid joints is proposed for frame-unit bamboo culm members, and the internal force sketches and calculation methods for bamboo culms and joints are presented, which can be used for the internal force analysis and design of frame-unit bamboo culm lattice structures.

The article is dedicated to addressing the current challenge of augmenting the load- bearing ca-pability of pile foundations. This predicament is most effectively addressed by employing piles with unconventional geometries, along with atypical methodologies for installing these foun-dation piles. The primary objective of research is to examine the impact of various fill materials (including both soil and rigid substances) on the energy consumption during pile driving and the resistance to static loads by piles with multiple shaft expansions. The findings derived from model-based investigations demonstrate that the load-bearing capacity of piles with shaft ex-pansions, installed with bulk material filling, surpasses that of conventional piles (prismatic and pyramidal) by a factor ranging from 1.5 to 4.6. Furthermore, the research outcomes also indicate greater energy consumption (1.14-1.66 times) and enhanced load-bearing capacity (1.15-1.68 times) for piles with shaft expansions driven with backfill, in comparison to piles installed without backfill. It is noteworthy that the type of backfill material significantly influences the energy consumption during pile driving and their stability under axial static loads. The correla-tion relationships can be applied to approximate projection of the energy-related and structural parameters of piles with shaft expansions embedded with the addition of bulk materials.

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment aims at the determinations of the correction coefficients of the mathematical model. The dot grid target is measured and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analysed. Uncertainties are evaluated with implementation of the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centres, K-means clustering, etc., are the same for both two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of lateral stage of confocal microscope is meaningful and practicable.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

Background. Rectal Magnetic Resonance Imaging (MRI) is a key test in advanced rectal cancer and in the preoperative staging of a lesion suitable for transanal endoscopic surgery (TES). MRI is not operator-dependent, but its results when determining anatomical landmarks are variable. Method. Observational study of inter-observer concordance regarding four diagnostic tests used to establish the anatomical characteristics of rectal lesions: colonoscopy, rectal ultrasound (EUS), rectal MRI, and intraoperative rigid rectoscopy (IRR) in patients scheduled for transanal endoscopic surgery (TES) with curative intent. This inter-observational study assessed the concordance between four expert radiologists regarding the topographic evaluation by means of rectal MRI of lesions under consideration for TES. Results. Fifty-five consecutive rectal tumors were studied. For most of the items, the correlation between IRR and colonoscopy or EUS was generally very good (intraclass correlation coefficient -ICC-)>0.75), although the correlation between MRI and IRR in relation to size by quadrants (ICC=0.092) and location by quadrants (ICC=0.292) was weak. The ICC for the other items obtained excellent correlations: Kappa index >0.80 for all items except for the distance from the peritoneal reflection to the anal verge, where it was merely good (IK=0.606). Conclusions. The anatomical description of rectal lesions that are candidates for TES provided by means of IRR, EUS, colonoscopy and MRI is reliable. The MRI is less reliable, but in the hands of expert radiologists, the anatomical study of rectal lesions is accurate and reproducible.

We investigated the radioclinical outcomes of naviculectomy and limited/tailored soft-tissue releases in a short series of ambulatory children with complex/intractable congenital vertical talus subsets namely neglected, multiple operated and recurrent patients. We postulated that this technique will yield satisfactory radioclinical outcomes and minimal complications because it avoids extensive surgical release/trauma that is otherwise classically recommended for complex congenital vertical talus (CVT). The cohort consisted of five -four boys, one girl- complex CVT children with neglected, multiple operated and/or recurrent subsets. Patients were included if manipulative casting techniques were deemed unlikely to produce a plantigrade foot. Patients underwent naviculectomy with variable on-demand limited soft tissue releases. Two patients had bilateral affection and two had a non-idiopathic aetiology. The mean age was 5.2 years (4 to 6.25) and mean follow-up was 2.3 years (1 to 3). We reported satisfactory outcomes as per foot posture, function, overall parent satisfaction including pain and radiography per lateral views of talar-axis-first metatarsal base angle on the short/intermediate term. Whereas manipulative casting is unlikely to yield lasting outcomes in ambulatory children with complex subsets of CVT, extensive surgical soft-tissue releases have unfavourable long-term complications. As a substitute, naviculectomy as a form of resection arthroplasty created a practical and affordable third way between manipulative casting with minimally invasive surgery and the extensive surgical soft tissue releases on the short/intermediate term.

This investigation introduces an efficient method for assessing the reliability of semi-rigid steel frame connections in existing buildings, explicitly targeting the Top Angle and Seat Pad (TA-SP) semi-rigid connection commonly used in Australian cities' high-rise buildings. The moment capacity of these connections was examined through parameter power model testing, meticulously considering the bending, shear, and prying forces actions to determine the weakest elements in the connection system. A plastic hinge model was applied to ensure computational efficiency and accuracy in assessing the connections' ultimate strength. Comparatively, the finite element (F.E) method M−θ curves were introduced to scrutinise the nonlinear behaviour of the connection, providing validation for the predicted analytical approach. Further emphasis was placed on identifying the reliability of the weakest elements in the connection system, employing the First-Order and Second-Order Reliability Methods models to estimate their reliability index. The correlation between the model's failure probability and a percentile error was also explored, utilising Monte Carlo simulation reference for refined validation. Novel formulas and methodologies were introduced to compute the locked-chain-series system reliability, which accounts for the inherent material and geometric variability. The findings highlight the critical significance of the weakest element in determining the overall reliability of the existing TA-SP connection.

This study investigates the application of deep residual networks for predicting the dynamics of interacting three-dimensional rigid bodies. We present a framework combining a 3D physics simulator implemented in C++ with a deep learning model constructed using PyTorch. The simulator generates training data encompassing linear and angular motion, elastic collisions, fluid friction, gravitational effects, and damping. Our deep residual network, consisting of an input layer, multiple residual blocks, and an output layer, is designed to handle the complexities of 3D dynamics. We evaluate the network's performance using a dataset of 10,000 simulated scenarios, each involving 3-5 interacting rigid bodies. The model achieves a mean squared error of 0.015 for position predictions and 0.022 for orientation predictions, representing a 25% improvement over baseline methods. Our results demonstrate the network's ability to capture intricate physical interactions, with particular success in predicting elastic collisions and rotational dynamics. This work significantly contributes to physics-informed machine learning by showcasing the immense potential of deep residual networks in modeling complex 3D physical systems. We discuss our approach's limitations and propose future directions for improving generalization to more diverse object shapes and materials.