On proper applications of Galërkin’s approach in structural mechanics courses

Under the background of engineering education accreditation and the development of new engineering disciplines, traditional structural mechanics courses are confronted with problems such as the disconnection between theory and practice, a monotonous teaching mode, and low student engagement. This study proposes a reform framework for structural mechanics courses that integrates interesting mechanics experiments. By Reconstructing teaching content, innovating teaching methods, and optimizing the evaluation system, a “theory-practice-political ideology” teaching model is constructed, providing strong support for better cultivating applied talents.

Due to the varying conventions for determining the sign of bending moments across different mechanics courses, particularly in elasticity mechanics where there are no clear guidelines, beginners often find themselves confused during the learning process. This inconsistency not only increases the difficulty of learning but also leads to confusion when students study across multiple disciplines. This paper analyzes and summarizes the sign conventions of various mechanical quantities and their interrelationships in different mechanics courses. By comparing the sign conventions of bending moments in these courses, this paper proposes a unified method for sign determination applicable to all of them and further validates the method's reasonableness and applicability through specific examples. Although researchers in recent years have proposed different methods for determining bending moments within specific disciplines, no one has yet introduced a theory that unifies the sign determination of bending moments across theoretical mechanics, structural mechanics, material mechanics, and elasticity mechanics. The findings of this research provide valuable insights for the teaching of mechanics courses.

In the new era of undergraduate education in China, around the purpose of cultivating first-class talents, it is necessary for the majority of educators to actively explore the deep integration of online and offline teaching. Based on the above background, the purpose of this research is to study the new teaching model of structural mechanics for civil engineering majors in the information age. This study introduces the construction of the online course of structural mechanics and the mixed teaching of structural mechanics for the structural mechanics teaching team of civil engineering majors in the university, and compares the structural mechanics of students participating in hybrid teaching with traditional teaching by statistical analysis of a large number of first-line construction data Final exam scores, compared with the final exam scores of the material mechanics course of the prerequisite course, analyze the advantages and disadvantages of mixed teaching on the improvement of students' academic performance; in addition, use various platforms to analyze the factors that affect the effect of mixed teaching, with a view to The continuous improvement of mixed teaching provides useful reference. Studies have shown that face-to-face teaching, online learning and classroom tests are the main factors that affect the effectiveness of mixed teaching. Among them, face-to-face teaching plays a key role in mixed teaching. Giving play to the guiding role of face-to-face teaching in classrooms, better completing online learning, and maintaining a good learning progress can help students better master the course learning content, which is conducive to the implementation of student-centered education concepts.

Fourth-order ordinary differential equations (ODEs) are applied in real-life situations such as analyzing the vibration and stability of structural elements, including beams, plates, and airplane wings. Other applications include modeling fluid flow, such as in the lungs, and the development of surface profiles in material science. In engineering, they are used in areas such as beam theory to predict beam failure and in analyzing the stress and strain in materials like reinforced concrete shells. The purpose of this study is to develop a class of continuous hybrid numerical methods for the direct solution of general fourth-order initial value problems of ordinary differential equations. The technique adopted in this work involves interpolation and collocation of a basis function and its corresponding differential system, respectively. The differential systems and the basis functions are collocated and interpolated, respectively, at selected grid and intra-step grid points. The unknown parameters in the system of linear equations arising from the collocation and interpolation procedures were determined, and the values were substituted into the approximate solution. The required continuous methods were obtained for different step numbers after the necessary simplifications. The derived methods were tested and found to be consistent, convergent, and to possess low error constants. The discrete schemes obtained from the continuous methods were implemented in block mode. The methods were applied to solve linear and nonlinear fourth-order initial value problems directly. The errors in the results obtained were compared with those of existing methods of the same and even higher order of accuracy to establish the superiority of the newly proposed method.

This paper explores innovative strategies and practical applications for teaching structural mechanics courses in the digital era. The focus is on analyzing how online-offline hybrid teaching models can optimize the educational process in structural mechanics and enhance teaching efficiency and student learning outcomes. The paper elaborates in detail on how digital technologies support the teaching of structural mechanics, including the use of various digital tools and platforms to foster student interaction and participation, as well as improve their understanding and mastery of course content. Additionally, the research discusses the effective integration of ideological and political education within structural mechanics teaching, aimed at fostering students' comprehensive abilities. This study provides new perspectives and methods for the teaching design of structural mechanics and related disciplines in a digital learning environment.

We present a survey of the results of investigations carried out by M. Ya. Leonov and his followers in the field of the theory of plasticity and its applications to the solution of boundary-value problems and problems of stability of rods, plates, and shells under simple and complex loading. It is shown that the influence of the memory of materials on the stability of structural elements can be significant. We also establish the relationship between the proposed theory of plasticity based on the concept of slip and the well-known theories of plastic flow and low elastoplastic strains.

In this paper, a model for teaching Structural Mechanics courses is presented. The model incorporates the use of a new teaching space as well as flipped-learning and collaborative activities including video production by the students. The results show that overall, the results show that the model improves students' satisfaction and more importantly, it has a positive effect on students' passing rate.

“Structural mechanics” is a professional basic course for civil engineering majors in Chinese universities. With the renewal of engineering education concept and the continuous improvement of social requirements for civil engineering professionals, the traditional structural mechanics teaching has gradually been unable to meet the learning needs of students. Taking the engineering certification in the new period as the guidance direction, reforming the teaching of structural mechanics and creating the “golden course” of structural mechanics have become the focus of teaching reform of civil engineering specialty in colleges and universities. This paper starts from the analysis of the problems existing in the teaching of structural mechanics, focusing on the teaching reform countermeasures of structural mechanics course, hoping to further optimize the teaching system of structural mechanics in colleges and universities, and cultivate more high-quality talents of engineering specialty.

REVIEWS 759 Professor Berend has given us a thought-provoking study. In any future edition, care should be taken that 'statnipravo' is not translatedas Rechtsstaat or Griinderzeit as the 'age of boosterism'. Anglo-American College, Prague Z. A. B. ZEMAN King, Jeremy. Budweisers intoCzechsandGermans. A LocalHistogyof Bohemian Politics, I848-I948. Princeton University Press, Princeton, NJ and London, 2002. XV+ 284 pp. Notes. Bibliography.Index. C27.95. THE flood of works now appearing on personal and communal forms of identityin the Habsburglands includes a growingstreamof treatmentswhich arguefor the survivalof markedlylocal loyaltiesmuch longer than historians' incautious use of phrases like 'national question' or 'ethnic contest' would suggest. Recent examples are Conrad Klewing's analysis of Dalmatia, EleonoraBabejov'a's of Pressburg,and the latest(2003) Austrian Histogy Yearbook articles on Galicia. Jeremy King has made a particularlysubtle, thoughtful and stimulatingcontribution to this sub-genre. His starting-pointis the year I848, the 'springtimeof nations', as the cliche has it. Yet most inhabitantsof the southern Bohemian municipality called alternatively Budweis or Ceske Budejovicewere, he claims, at that time stillneither German nor Czech, but literally 'Budweisers',probably knowing both the languages which gave the two differentnames to their town, and feeling attachment to the place itself, ratherthan to any largernational community. Underpinning that stance was a traditionalcommitment to the ethnically neutral dynasty and its authorities; and these continued to moderate and arbitrate the clash of rival national camps over the next half-century and more. Some of King's most insightfulpages are devoted to party politics in Budweis, constantlyrefractedby native concerns, splinteringand regrouping as domestic issues were negotiated by the organs of executive and legislative power within Austriain the constitutionalera. Although explicit German and Czech allegiances gained ground, they suffered from their own internal divisions and from the continuing equivocation or amphibiousness of significant sections of society. On the eve of World War I a settlement roughlyon the lines of the largerMoravian compromiseof I 905 was about to be enacted in Budweis, recognizing the need for rival national selfidentifications ,yet witnessing to the scope for local solution of the resultant problems. The collapse of the Monarchy ostensibly left (besides a small Jewish community, now counted separately)only Czechs and Germans with the former in control. The number of 'Germans', i.e. of first-languageGermanspeakers , in Ceske Budejovice even fell below the 20 per cent threshold necessary for linguistic rights. Yet, King contends, there was still no straight duality especially when Hitler's Reich emerged from 1933 to complicate German loyaltieswithin and beyond Czechoslovakia.In the years from I938 onwards, numerous citizens trimmed with the political wind, declaring or seeking to declare themselves Germans during the time of the Protectorate and Czechs when expulsion threatened in I945. Ironically, the replacement of an ethnicby a racialcriterionfornationalallegiancenow fora spellrestored 760 SEER, 82, 3, 2004 some of the flexibilitywhich previous curial arrangementshad eliminated except, of course, for theJews. King brilliantlydemonstratesthe complexities and ambiguitiesinvolved in the ascriptionof ethnicity according to objective or subjectivecriteria,as the case might be, and the ways in which these were marshalledto servecompeting nationalprogrammes. Yethispurestsubject-matterremainstantalizinglyin the shadows.'Budweisers ', as King freely admits, are difficultto identify, as is the extent of that bilingualismwhich formed their prime defining characteristic.This seems to have been widespreadin Budweis,but littleclear evidence is suppliedfor it or for the intriguingsuggestionof the use there of a mongrel patois or pidgin. Censuses cast scarcely any light on the matter, since they allowed only one language to be recorded. It is probably impossible anyway, as we know from the imponderability of similar kinds of statisticselsewhere (e.g. those nearer home about knowledgeof Welsh),to measurewith any accuracythe sphereof application of such submerged vernaculars and the nature of associated linguistic symbiosis. Hardly easier to assess are the social and political implications. King's own sources may leave us wondering whether many Budweisers were really so ethnically indifferent, when as early as thei86os even culturalassociationslikethe town'schoirswere alreadyrivenby national strife, and when by the turn of the century mob violence became commonplace . The author's reliance on the local press, which usually had an axe to grind, may actuallyundercut his own argument here. And perhaps he is also too ready to assume the impartialityof all those...

The capability of organizations to respond to unexpected events has been investigated from different theoretical angles: organizational learning, improvisation, ambidexterity, resilience, to name but a few. These concepts, however, hardly ever refer to structural characteristics. Against this backdrop, the aim of this paper is twofold. First, based on systems and organizational learning theory, it will theoretically link the characteristics of organizational structure with organizational responses to unexpected external jolts, thus contributing to better understand the reactions of organizations to the unexpected. Second, it will empirically illustrate the relation of organizational structure with organizational responses by investigating how Civil Society Organizations (CSOs) in Austria reacted to the unexpected inflow of refugees from Central Europe. In 2015, CSOs accepted a wide range of responsibilities and worked together with government entities to provide shelter, catering, and transport for almost one million refugees. Based on participant observations during operation, in-depth interviews (2015 and 2016) and focus groups with decision-makers (2017), we will sketch three longitudinal case studies of organizations with very different structures, concentrating on the processes and operations they developed during the crisis. Our findings show that their responses are closely related to their structure, specifically to the flexibility and the stability of structural elements. Remarkable changes took place in all organizations investigated. Initial responses and first structural changes occurred mainly where the structure already allowed for flexibility. Yet in the long run, the adaptations also impacted the stable structural elements.

The problem of stability and buckling of plates under creep conditions has been studied in the fundamental papers [1–4]. In the papers [5, 6], the theory of buckling of rods and plates is developed in the framework of the dominating bending model [7], where the forces in the midplane of the plate were determined independently of the solution of the bending problem. In what follows, we use the Karman scheme [8] to derive two basic differential equations of the coupled theory of the plane stress state and bending. We solve the problem of buckling of a rectilinear plate for linearly viscous (Newtonian) medium and show that the Karman scheme gives an essential correction to the solution of the bending problem for initial deflections comparable with the plate thickness.

Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity

This comprehensive textbook compiles cutting-edge research on beams and circular plates, covering theories, analytical solutions, and numerical solutions of interest to students, researchers, and engineers working in industry. Detailing both classical and shear deformation theories, the book provides a complete study of beam and plate theories, their analytical (exact) solutions, variational solutions, and numerical solutions using the finite element method. Beams and plates are some of the most common structural elements used in many engineering structures. The book details both classical and advanced (i.e., shear deformation) theories, scaling in complexity to aid the reader in self-study, or to correspond with a taught course. It covers topics including equations of elasticity, equations of motion of the classical and first-order shear deformation theories, and analytical solutions for bending, buckling, and natural vibration. Additionally, it details static as well as transient response based on exact, the Navier, and variational solution approaches for beams and axisymmetric circular plates, and has dedicated chapters on linear and nonlinear finite element analysis of beams and circular plates. Theories and Analyses of Beams and Axisymmetric Circular Plates will be of interest to aerospace, civil, materials, and mechanical engineers, alongside students and researchers in solid and structural mechanics.

In this paper, a teaching model that makes use of a YouTube video repository for Engineering courses is presented. Some results show the preference of students of such a model over traditional teaching models that use live video. The proposed offline model with a video repository is presented as a better alternative for Engineering courses, improving aspects as students satisfaction and above all, the performance of students in Structural Mechanics courses where the model was implemented.

This work presents the latest results on how to successfully apply a hybrid and flexible model for teaching Engineering Courses, particularly Structural Mechanics courses to students from Architecture and Civil Engineering programs during emergency conditions such as those due to the Covid19 Pandemic. During the first term of the year 2020, most universities around the world had to move to an online teaching model. In the case of our university, the first term of 2020 had started on campus on February 7th and it was during mid-March that the decision was made o go fully online, based on nation wide cases of Covid19 being confirmed. Our university was the first university making such a move in Mexico and in order to prepare for the online model, a week was given to all professors and instructors to adapt their courses before going fully online on the third week of March, 2020. In the case of the courses being currently taught by one of the authors of this work, they were already being taught in a hybrid manner, combining asynchronous offline sessions with synchronous sessions in the classroom. This model has been used for the last few years with tremendous success in the performance of the students and their overall satisfaction as it has been shown in [1]. For the pandemic conditions, the synchronous sessions were changed from the classroom on campus to the online classroom with videoconferencing. Some new types of activities were included for online teaching such as video documentaries and also some modifications were made to the standard synchronous sessions, which are also discussed in this work. A total of 135 students have taken the courses that use this model during the spring term, summer term and fall term of 2020. The students come from different cities across Mexico and are located in three different time zones. These students answered a survey that include several aspects of the online experience: problems faced by students when connecting online, type of connections available at their homes, preferred type of sessions, courses that are better suited for online teaching and their personal experience with the course, among others. This paper shows the results of the analysis of the questions answered by the students and some important graphs are included. Some recommendations are also given that future implementations of hybrid and flexible (HyFlex) models can take into account for a better overall experience of both, students and professors. This model can also be applied for the new normality where some toggle terms are expected, that this, some weeks on campus and some weeks with online teaching as new covid19 cases are detected in each region.