Mechanical Problems Research Articles

Hypersingular Integral Equations Encountered in Problems of Mechanics

In the paper, for hypersingular integral equations with new kernels, a solution is constructed using an approach based on Chebyshev orthogonal polynomials and the principle of contraction mappings. Integrals in hypersingular integral equations are understood in the sense of Hadamard finite-part integrals. The hypersingular integral equations under consideration in some cases of kernels are solved exactly in closed form using the Chebyshev orthogonal polynomial method, and with other kernels by the same method, they are reduced to infinite systems of linear algebraic equations. In addition, hypersingular integral equations with the kernels considered in the article are reduced to finite systems of linear algebraic equations using Gauss–Chebyshev type quadrature formulas. To assess the effectiveness of the two methods, a comparative analysis of the results for hypersingular integral equations with the corresponding kernels is carried out.

The Determinacy Problem in Quantum Mechanics

Of the many ways of getting at the core of the weirdnesses in quantum mechanics, there’s one which traces back to Schrödinger’s seminal 1935 paper, and has to do with the apparent fuzzy nature of the reality described by the formalism through the wavefunction ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi$$\\end{document}. This issue, which I will be calling the Determinacy Problem, is distinct from the standard measurement problem of quantum mechanics, despite Schrödinger himself ends up conflating the two. I will argue that the Determinacy Problem is an exquisitely philosophical problem, for as it is standard when facing any phenomenon which appears to have indeterminate or fuzzy characteristics, the solutions available are to either blame the deficiencies of our language, or our lack of knowledge, or to blame the world itself. These three attitudes can already be found in the literature on quantum mechanics, either explicitly or implicitly, and they appear to motivate three very distinct research programs: high-dimensional realism, primitive ontology, and quantum indeterminacy.

Peculiarities of formation and processing of surface interferograms according to Twyman-Green scheme in non-destructive testing

The goal of the work is to ensure the maximum accuracy of reconstruction of relief and de-formation displacement fields of structural element surface by the interferometric method. The authors successfully use novel algorithms for the processing of surface interferograms as well as the interferometers that follow the Twyman-Green scheme in order to implement such opti-cal testing of the surface. The maximum precision of obtained experimental data was achieved by the use of structural additions to the optical circuit and the selection of optical elements and their settings during adjustment of the interferometer, as well as new algorithms for the selec-tion and registration of a series of interferograms, speckle interferograms and speckle surface images. The authors proposed structural additions to the interferometer scheme used in the testing of both smooth and rough surfaces, appropriate methods for calculating the parameters of optical elements and their adjustments. Examples of obtained interferograms of the surface of metals under the static and fatigue cyclic loading, speckle interferograms of the surface of metals and polymer composites under the static and dynamic loading are given. The results of processing and interpreting these interferograms confirm that the Twyman-Green interfero-meter is an effective instrument for solving the problems of fracture mechanics and deformable solids. In particular, an assessment was made of: roughness and waviness of the surface of metals; sizes of the plastic zone around the stress concentrator; deformation displacement fields of metals and composites, as well as the detection of hidden defects in them.

Pelatihan Aplikasi SAP2000 Untuk Meningkatkan Kemampuan Dalam Penyelesaian Problem Mekanika Teknik Bagi Siswa SMKN 2 Surabaya

In accordance with Presidential Instruction (Inpres) Number 9 of 2016 concerning the Revitalization of Vocational High Schools (SMK) in the context of Improving the Quality and Competitiveness of Indonesian Human Resources (HR), it is necessary to compile a map of labor needs for SMK graduates according to their respective duties, functions, and authorities based on the road map for vocational development. One of the targeted developments is the skill of using computer applications in accordance with its basic competencies. Currently, engineering mechanics lessons at SMKN 2 Surabaya are only given theoretically. The use of computer applications to help solve existing problems has not been implemented. Even though work challenges today really require these skills to solve more complicated problems, more quantities, and faster solutions. Based on the above, this PKM activity aims to improve students' ability to use SAP2000 applications to solve engineering mechanics problems. The training provided includes an introduction to the basic use of SAP2000 including the use of the menus in it. Followed by the practice of working on example problems along with discussing their theoretical validation. After that, exercises for more complicated problems are given which end with giving quizzes to further motivate students. From the post-test results given at the end of the training, the results showed that 85.58% of trainees could understand the training material well. This shows that this training is very effective in improving students' abilities which is expected to bring benefits as a provision to face work challenges after graduation.

Study on grain refinement of AlB2 structure in aluminium alloys

ABSTRACT Aiming at the problem of unclear grain refinement mechanism in aluminium alloys, Al n B n (n = 2–12) clusters and Al–3B alloy were studied by density functional theory methods. The results show that as the cluster size increased, B atoms self-aggregated, and Al atoms surrounded the surface of the clusters. In addition, Al and B atoms formed stable AlB2 triangular structures. The average binding energy gradually increased with increasing clusters size, which indicated that the clusters structures were gradually stable. Range of n = 2–11, the Al9B9 cluster showed the most stable structure. Electronic properties and interatomic interactions calculation results suggested that there was a minimum electrostatic potential point on the surface of the B atom, and the B atom in AlB2 may be the adsorption site of α-Al. The ab initio molecular dynamics simulations results of the Al–3B alloy showed that Al and B generated the AlB2 structure in situ, and Al atoms nucleated and grew on the AlB2 surface. These results can be used to understand the grain refinement mechanism of the Al–B intermediate alloy.

Physics-informed two-tier neural network for non-linear model order reduction

In recent years, machine learning (ML) has had a great impact in the area of non-intrusive, non-linear model order reduction (MOR). However, the offline training phase often still entails high computational costs since it requires numerous, expensive, full-order solutions as the training data. Furthermore, in state-of-the-art methods, neural networks trained by a small amount of training data cannot be expected to generalize sufficiently well, and the training phase often ignores the underlying physical information when it is applied with MOR. Moreover, state-of-the-art MOR techniques that ensure an efficient online stage, such as hyper reduction techniques, are either intrusive or entail high offline computational costs. To resolve these challenges, inspired by recent developments in physics-informed and physics-reinforced neural networks, we propose a non-intrusive, physics-informed, two-tier deep network (TTDN) method. The proposed network, in which the first tier achieves the regression of the unknown quantity of interest and the second tier rebuilds the physical constitutive law between the unknown quantities of interest and derived quantities, is trained using pretraining and semi-supervised learning strategies. To illustrate the efficiency of the proposed approach, we perform numerical experiments on challenging non-linear and non-affine problems, including multi-scale mechanics problems.

Application of machine learning for ‘what if?’ stress analysis

Analysis of stresses in components of even modestly complex geometries often require the use of finite element analysis (FEA). For testing a large number of design options quickly, FEA can be time consuming and provides more accuracy than required. In this project, a machine learning-based system is developed to provide quick and approximate solutions to stress analysis problems in parametrised compressor disc geometries. Simple mechanics problems were completed preliminarily to test the practicality of machine learning approaches for this application. This included applying instance selection by the [Formula: see text]-medoids algorithm to a 2D FEA problem. A parametrised compressor disc geometry was designed and defined by eight dimensions. Stress fields were produced from two superimposed loading schemes: the rotational body force and the force exerted on the disc by the blades 495,338 samples of training data were collected from 4374 FEA simulations. Four networks were trained to predict stresses caused by each loading scheme in order to produce stress fields. The best network was of the structure 9/20/20/2 and used normalised training data. For the geometry tested, it predicted stresses with a root-mean-square error of 1.51%. The code took 0.7 s to run in total, from start-up to completion of a stress plot. The importance of the inputs in the training data set were scored with a feature selection algorithm to aid further optimisation of the system. The low computation time makes this system suitable for the early stages in a design process.

Effects of conical singularity and Wu-Yang magnetic monopole on thermodynamic properties of harmonic oscillator interacting with potential

Abstract This paper investigates the thermodynamic properties of the harmonic oscillator system in a conical singularities background. Moreover, we incorporate a Wu-Yang magnetic monopole (WYMM) and inverse square potential into the quantum system and analyze the resulting effects. Using analytical methods, we derive the energy eigenvalues and study the thermodynamic properties, such as the partition function, Helmholtz free energy, Gibbs's free energy and specific heat capacity at finite temperature $T \neq 0$. Our findings demonstrate that these physical parameters are influenced by the topological parameter, strength of WYMM and potential parameters. These results provide valuable insights into the interplay between thermodynamic properties of a quantum mechanical problem and the gravitational effects.

Implementation and Application of Cell-Based S-FEM Based on the Object-Oriented Programming Framework

The object-oriented programming is widely used in different fields of finite element analysis (FEA). The commonly used object-oriented codes were almost written by C++. Due to the inability to automatically manage memory and the lack of gigantic standard library and a third-party library for C++, building matrix classes are needed and a strong programming ability for program developers is also necessary. The conventional FEM method still has many disadvantages such as poor accuracy, hard stiffness matrix, mesh dependence and lack of upper bound solution. The smoothed FEM (S-FEM) method proposed by Liu et al. can efficiently overcome these disadvantages and is therefore widely used in FEA. In this work, the elastic-plastic CS-FEM method is extended and implemented using Python programming based on the framework proposed [H. Li and Y. Xiao, Implementation and numerical simulation on object-oriented elastic-plastic finite element method based on Python, J. Syst. Simul. 36(5) (2024) 1107–1117] The resulting object-oriented elastic-plastic CS-FEM framework is then applied to FEA of elastic-plastic mechanics problems. The correctness of the resulting framework and the high computational accuracy and good mesh adaptability of CS-FEM models have been verified by comparing the corresponding results with an analytical solution or ABAQUS results. The object-oriented elastic-plastic CS-FEM framework provides a more efficient and adaptable approach to FEA, and can also overcome many limitations of the conventional FEM method and C++ programming. The use of Python and the CS-FEM method offers improved computational accuracy, mesh adaptability and development efficiency, and this will make it a valuable tool for solving practical problems in mechanics and engineering.

The mixed displacement method to avoid shear locking in problems in elasticity

AbstractThe mixed displacement (MD) method was initially developed to mitigate geometrical locking effects in beams, plates, and shells with the intention of having intrinsically locking‐free characteristics while using equal‐order interpolation for all degrees of freedom. In other words, it is an unlocking scheme that works independent of the element shape, polynomial order, and discretization scheme. It includes additional degrees of freedom that adhere to a carefully designed differential relation that can be interpreted as a kinematic law, incorporated in a mixed sense. Certain constraints are to be enforced on these additional degrees of freedom to obtain a well‐posed system of equations. In this work, the MD method is extended for problems in solid mechanics. We present the underlying variational formulation, followed by its application to 2D solid elements. Additionally, we showcase an idea to enforce the additional constraints in a general sense. Various numerical examples, within the framework of the finite element method and isogeometric analysis, are outlined to demonstrate the performance of the MD method in the geometrically linear and geometrically nonlinear cases.

Compatibility of strains and the three-fold differentiability of the displacement field

The problem of the necessary class of smoothness of solutions to quasi-static problems of deformable solid mechanics in terms of displacements was discussed. It is shown that in order for the equations of compatibility of deformations to become identities when displacements are substituted in them, the existence of some third mixed derivatives of displacements is required. A counterexample for a linearly elastic compressible isotropic elastic medium was given. In this counterexample, the displacement field, being a doubly differentiable solution to the boundary value problem for the system of Lame equations in the entire domain, is not a solution to the displacement problem at all points in this domain.

Perinatal care in the earthquake disaster of the century: Nurses' and midwives' experiences.

To determine the experiences of nurses and midwives providing perinatal care in an earthquake area. On February 6, 2023, two earthquakes measuring 7.8 and 7.6 magnitudes struck Turkey, affecting a large area. It is crucial for perinatal care to be rapidly organized, provided under the most suitable conditions, and delivered by qualified health professionals. Understanding the post-disaster experiences of nurses and midwives is crucial to addressing this issue. This is a qualitative study using phenomenological methodology with 8 nurses and 12 midwives in the earthquake-affected area. Personal information and semistructured interview forms were used for data collection. Content analysis was used for data analysis. Participants had a mean age of 33.75 years. The experiences of nurses and midwives were grouped into five themes: emotions experienced, challenges encountered, problems in perinatal services, coping mechanisms, and recommendations. The emotions experienced theme encompasses both positive and negative emotions. The challenges encountered theme includes challenging environmental conditions, organizational issues, problems with medical supplies and drugs, and being a victim of the earthquake. The problems in perinatal services theme includes pregnancy, childbirth, and postpartum services. The coping mechanism's theme encompasses problem-focused and emotion-focused coping strategies. The recommendations theme includes education and awareness, preparedness for disasters, and sustainable services. Nurses and midwives working in the earthquake-affected area experienced numerous physical and psychological challenges and encountered difficulties in delivering health services. Adisaster educationcourse including simulated disaster drills and practice can be integrated into the education system. Strengthening healthcare facilities against disasters and raising awareness among the community are crucial.

The cohesin complex: structure and principles of interaction with dna

Accurate duplication and separation of long linear genomic DNA molecules is associated with a number of purely mechanical problems. SMC complexes are key components of the cellular machinery that ensures decatenation of sister chromosomes and compaction of genomic DNA during division. Cohesin, one of the essential eukaryotic SMC complexes, has a typical ring structure with intersubunit pore through which DNA molecules can be threaded. The capacity of cohesin for such topological entrapment of DNA is crucial for the phenomenon of post-replicative association of sister chromatids better known as cohesion. Recently, it became apparent that cohesin and other SMC complexes are in fact motor proteins with a very peculiar movement pattern leading to the formation of DNA loops. This specific process was called loop extrusion. Extrusion underlies multiple cohesin’s functions beyond cohesion, but the molecular mechanism of the process remains a mystery. In this review, we have summarized data on the molecular architecture of cohesin, the influence of ATP hydrolysis cycle on this architecture, and the known modes of cohesin–DNA interactions. Many of the seemingly disparate facts presented here will probably be incorporated in a unified mechanistic model of loop extrusion in a not so far future.

Exploring electron-phonon coupling using quantum computing methods

Abstract Quantum computing in the noisy intermediate-scale quantum (NISQ) era has foregrounded the importance of Variational Quantum algorithms (VQAs). These algorithms are crucial for addressing complex quantum mechanical problems that challenge classical computers. One such problem is the electron-phonon (e-ph) interaction, which is essential for determining the zero-point renormalization (ZPR) of electronic structure properties. The calculation of ZPR of fundamental gap relies on the accurate computation of ionization potential (IP) and electron affinity (EA) energy levels in molecular systems, where the VQAs offer the promising solutions. Despite the critical importance of IP, EA energies and ZPR in quantum chemistry calculations, research into the application of quantum algorithms for these calculations remains limited. To address these challenges, we propose two quantum algorithms for ZPR of fundamental gap calculation using Variational Quantum Deflation (VQD) and Quantum equation of Motion (QEOM) algorithm for several molecular systems. This work opens up new possibilities for the accurate and efficient study of e-ph interaction in electronic structure calculations, even with NISQ-era hardware.

Challenges in sensemaking and reasoning in the context of degenerate perturbation theory in quantum mechanics

We discuss an investigation of student sensemaking and reasoning in the context of degenerate perturbation theory (DPT) in quantum mechanics. We find that advanced undergraduate and graduate students in quantum physics courses often struggled with expertlike sensemaking and reasoning to solve DPT problems. The sensemaking and reasoning were particularly challenging for students as they tried to integrate physical and mathematical concepts to solve DPT problems. Their sensemaking showed local coherence but lacked global consistency with different knowledge resources getting activated in different problem-solving tasks even if the same concepts were applicable. Depending upon the issues involved in the DPT problems, students were sometimes stuck in the “physics mode” or “math mode” and found it challenging to coordinate and integrate the physics and mathematics appropriately to solve quantum mechanics problems involving DPT. Their sensemaking shows the use of various reasoning primitives. It also shows that some advanced students struggled with self-monitoring and checking their answers to make sure they were consistent across different problems. Some also relied on memorized information, invoked authority, and did not make appropriate connections between their DPT problem solutions and the outcomes of experiments. Advanced students in quantum mechanics often displayed analogous patterns of challenges in sensemaking and reasoning as those that have been found in introductory physics. Student sensemaking and reasoning show that these advanced students are still developing expertise in this novel quantum physics domain as they learn to integrate physical and mathematical concepts. Published by the American Physical Society 2024

Focal mechanism determination by location-constrained deep learning: application to microseismic monitoring

Accurate and rapid determination of focal mechanism solutions is of great significance for real-time seismic monitoring. Previous deep learning approaches for focal mechanism determination typically use the waveform data, which is sensitive to the velocity model and inherently includes information about both the source location and the focal mechanism. We introduce a location-constrained deep learning algorithm for determining the focal mechanism for surface microseismic events. By using aligned P-wave data along with azimuth and take-off angle as input, we narrow the solution space for the focal mechanism problem and reduce the dependence on the velocity model. The model is trained using 40,000 theoretical samples generated with the geometry and velocity model of the field data. Validation tests, comparisons with a waveform-based network, velocity perturbation tests, and location error tests are performed to demonstrate the robustness and efficiency of our method. After applying the trained model to field data, the results demonstrate that our method is fast and achieves comparable accuracy to HASH results for high-quality events, making it promising for real-time microseismic monitoring.

Examining mechanics problem-solving strategies among engineering students at a selected public university in Rwanda

Abstract This paper presents the findings of research conducted at a selected university in Rwanda aiming to evaluate the mechanics of problem-solving strategies among engineering students. Problem-solving is an important component of science, technology, engineering, and mathematics education as well as in everyday life. To enhance the development of problem-solving skills, researchers and curriculum creators must develop problem-solving strategies for solving mechanics problems and for improving engineering students’ performance in physics classroom tasks. The study investigated engineering students’ strategies for their mechanics problem-solving using a mixed-methods research approach that includes questionnaires, interviews, and tests. A purposive sample of 99 students was chosen, with 20 students and three instructors randomly selected for interviews. Findings revealed that students heavily rely on algebraic equations, neglecting visual representations in mechanics problem-solving. Challenges identified include limited familiarity with alternative representations, difficulties transitioning between them, and a constrained understanding of their interrelationships. Recognizing these practices and strategies informs the design of more effective pedagogical interventions. Incorporating the best problem-solving strategies in physics education is a potential avenue to bolster problem-solving skills and deepen comprehension of mechanics concepts among engineering students.

Generation characteristics and molecular reaction dynamics mechanism of PAHs during oxygen-lean combustion of jet coal

Severe coalfield fires occur in China, mainly in the northwest provinces of Xinjiang, Inner Mongolia, and Ningxia. Among the organic pollutants produced by oxygen-lean combustion, PAHs are considered one of the most dangerous pollutants due to their environmental contamination and “carcinogenic, teratogenic, and mutagenic” effects on human beings. In this paper, to address the problems of PAHs generation and reaction mechanism in coalfield fire, the jet coal from Xinjiang Zhundong Coalfield was selected to conduct the experiments, and the combustion products were detected using GC–MS and FTIR. The molecular dynamics method based on the reaction force field was also used to calculate the reaction process of 17 single molecules (5083 atoms) of jet coal combusted from 300 K to 4000 K at 0.5 oxygen equivalent ratio. The experimental results show that the generation of PAHs increased roughly from 573 K to 773 K at the three oxygen concentrations, and an increase in oxygen content can enhance PAHs generation to some degree. The structural evolutions and product changes in the system have been traced, and it is also clarified that the reaction history of oxygen-lean combustion mainly experiences two stages: thermal decomposition of coal structure and transformation of aromatic structure. The generation mechanism of PAHs is proposed from the perspective of molecular reaction dynamics. On the one hand, it is due to the breakage of active sites such as C-S, C-O, and O-H during the decomposition of coal structure. On the other hand, it originates from the polycondensation reaction triggered by the dehydrogenation of aromatic structure that enlarges the aromatic dimension. The research results reveal the generation characteristics and reaction pathways of PAHs in the oxygen-lean combustion of low-rank coal in the fire zone and provide certain references for coal fire management and pollutant control.

Variational inequalities of multilayer elastic contact systems with interlayer friction: Existence and uniqueness of solution and convergence of numerical solution

Inspired by the layered structure models in pavement mechanics research, in this study, a class of multilayer elastic contact systems with interlayer frictional contact conditions and deformable supporting frictional contact conditions on the foundation has been constructed. Based on the nonlinear elastic constitutive equations, the corresponding system of partial differential equations and variational inequalities are respectively introduced. Under the framework of variational inequalities, the existence and uniqueness of solutions for such models, along with the approximation properties of finite element numerical solutions, are proven and analyzed. The aforementioned conclusions provide fundamental and broadly applicable theoretical support for addressing mechanical problems in multilayer elastic contact systems within the framework of variational inequalities. Finally, the numerical experimental results based on the mixed finite element method also substantiate our theoretical conclusions.

Multi-level physics informed deep learning for solving partial differential equations in computational structural mechanics

Physics-informed neural network has emerged as a promising approach for solving partial differential equations. However, it is still a challenge for the computation of structural mechanics problems since it involves solving higher-order partial differential equations as the governing equations are fourth-order nonlinear equations. Here we develop a multi-level physics-informed neural network framework where an aggregation model is developed by combining multiple neural networks, with each one involving only first-order or second-order partial differential equations representing different physics information such as geometrical, constitutive, and equilibrium relations of the structure. The proposed framework demonstrates a remarkable advancement over the classical neural networks in terms of the accuracy and computation time. The proposed method holds the potential to become a promising paradigm for structural mechanics computation and facilitate the intelligent computation of digital twin systems.