Pub Date : 2022-08-28DOI: 10.37538/0039-2383.2022.4.24.28
S. V. Bosakov, O.V. Kozunova2
The paper presents new possibilities of using a mixed method for calculating bendable plates with complex boundary conditions. When composing resolving equations, it is sufficient to have an expression to determine the deflections of a plate with a normal pinched at the origin. Such solutions are given in the authors’ previously published works for plates of various shapes. On the basis of these solutions, the canonical equations of the mixed method are compiled, where the unknown forces of the method are the forces in the support links, the displacement method is linear and angular displacement of the pinching introduced at the origin. After determining the unknown forces of the method, according to the generally accepted formulas of the mixed method, the deflections of the plate are determined, according to which, in turn, internal forces are determined. Two examples of calculating plates in Cartesian and polar coordinates are given. Numerical implementation of the proposed methodology and algorithm for elastic calculation of bendable plates with complex boundary conditions is carried out using the Wolfram Mathematica 11.3 computer program.
{"title":"Mixed method for calculations of plates with complex boundary conditions","authors":"S. V. Bosakov, O.V. Kozunova2","doi":"10.37538/0039-2383.2022.4.24.28","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.4.24.28","url":null,"abstract":"The paper presents new possibilities of using a mixed method for calculating bendable plates with complex boundary conditions. When composing resolving equations, it is sufficient to have an expression to determine the deflections of a plate with a normal pinched at the origin. Such solutions are given in the authors’ previously published works for plates of various shapes. On the basis of these solutions, the canonical equations of the mixed method are compiled, where the unknown forces of the method are the forces in the support links, the displacement method is linear and angular displacement of the pinching introduced at the origin. After determining the unknown forces of the method, according to the generally accepted formulas of the mixed method, the deflections of the plate are determined, according to which, in turn, internal forces are determined. Two examples of calculating plates in Cartesian and polar coordinates are given. Numerical implementation of the proposed methodology and algorithm for elastic calculation of bendable plates with complex boundary conditions is carried out using the Wolfram Mathematica 11.3 computer program.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116702543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.14.17
V. A. Komarov, D. Yerkin
Rod models for assessing the strength of compressed concrete strips under the action of a cut of short cantilevers of crossbars between the supporting and “conditional” cargo platforms are proposed based on modeling their physical work. The basis for improving the calculation method is a single principle for constructing rod models of compressed concrete strips of short elements – there is the method of copying the trajectories of force cracks and fracture patterns. The improvement of the calculation method was carried out on the basis of the development of the above-considered method for determining the strength of concrete strips under the action of compression along an inclined strip and the action of a cut between the faces of the cargo and support platforms inside the compressed strip. In the process of improving practical recommendations for the calculation, the patterns of modification of rod models under the action of compression and shear were used, depending on the change in the main factors. All proposals for the calculation are brought to the level of practical application and are substantiated by experiment.
{"title":"Rode models of the cut of compressed concrete strips of the cantilever supports of the beams of multi-storey frameworks","authors":"V. A. Komarov, D. Yerkin","doi":"10.37538/0039-2383.2022.3.14.17","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.14.17","url":null,"abstract":"Rod models for assessing the strength of compressed concrete strips under the action of a cut of short cantilevers of crossbars between the supporting and “conditional” cargo platforms are proposed based on modeling their physical work. The basis for improving the calculation method is a single principle for constructing rod models of compressed concrete strips of short elements – there is the method of copying the trajectories of force cracks and fracture patterns. The improvement of the calculation method was carried out on the basis of the development of the above-considered method for determining the strength of concrete strips under the action of compression along an inclined strip and the action of a cut between the faces of the cargo and support platforms inside the compressed strip. In the process of improving practical recommendations for the calculation, the patterns of modification of rod models under the action of compression and shear were used, depending on the change in the main factors. All proposals for the calculation are brought to the level of practical application and are substantiated by experiment.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115216327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.55.60
A. I. Pritykin
Influence of perforation on the lateral-torsional buckling of I-beams with plane and castellated web in elastic stage of loading was considered with help of the finite element method, which allow to analyze critical loads of castellated beams and beams with plane web. Calculations were performed for simply supported beams under uniformly distributed load and concentrated forces, applied symmetrically at different distances from supports. Numerical calculations were carried out with help of program complex ANSYS on specially elaborated program. For castellated beams under constant relative depth of openings there were varied such parameters as shape and step of openings. Performed comparison of results with existing in literature analytical calculations of beams with plane web allow to confirm accuracy of existing formulas.
{"title":"FINITE-ELEMENT ANALYSIS OF LATERAL-TORSIONAL BUCKLING OF BEAMS WITH PLANE AND CASTELLATED WEB","authors":"A. I. Pritykin","doi":"10.37538/0039-2383.2022.3.55.60","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.55.60","url":null,"abstract":"Influence of perforation on the lateral-torsional buckling of I-beams with plane and castellated web in elastic stage of loading was considered with help of the finite element method, which allow to analyze critical loads of castellated beams and beams with plane web. Calculations were performed for simply supported beams under uniformly distributed load and concentrated forces, applied symmetrically at different distances from supports. Numerical calculations were carried out with help of program complex ANSYS on specially elaborated program. For castellated beams under constant relative depth of openings there were varied such parameters as shape and step of openings. Performed comparison of results with existing in literature analytical calculations of beams with plane web allow to confirm accuracy of existing formulas.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132893088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.42.48
V. Mondrus, L. Stupishin
The article analyses the stability of systems with lumped parameters from the standpoint of the criterion of critical energy levels. Until now, there is no consensus both on the reasons for the manifestation of the buckling of the deformation form in building structures, and on the formulation of criteria that determine the critical state. Most often in structural mechanics and the theory of stability of structures, energy criteria are used in the form of Timoshenko and Brian. Despite the simplicity of the formulation of the first criterion and the generality of the second, it is difficult to assert that they can cover the entire spectrum of stability problems that arise in technology. The criterion of critical energy levels allows one to set and solve stability problems without restrictions on the smallness of displacements, the type of impact on the system, and is intended for formulating boundary states. To understand the essence of the mentioned criteria and to illustrate the differences, simple problems are proposed in the form of systems with lumped parameters with several degrees of freedom. The design research technique is illustrated by the example of a system model with lumped parameters in the form of elastic hinges. Energy relations are given that describe the state of the system at critical energy levels. The results obtained for critical internal forces coincide with the values of external critical loads known from the literature, which confirms the well-known fact of the theory of eigenvalue problems that the branch points of the solution coincide in linear and nonlinear formulations. A technique for determining the values of the deviation angles of the system elements in elastic hinges is shown. A comparison is made of the rotation angles of the system elements in the formulation of the problem in a linear (infinitely small deviation angles) and non-linear formulation.
{"title":"Stupishin investigation of the stability of systems with lumped parameters based on critical energy level criterion","authors":"V. Mondrus, L. Stupishin","doi":"10.37538/0039-2383.2022.3.42.48","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.42.48","url":null,"abstract":"The article analyses the stability of systems with lumped parameters from the standpoint of the criterion of critical energy levels. Until now, there is no consensus both on the reasons for the manifestation of the buckling of the deformation form in building structures, and on the formulation of criteria that determine the critical state. Most often in structural mechanics and the theory of stability of structures, energy criteria are used in the form of Timoshenko and Brian. Despite the simplicity of the formulation of the first criterion and the generality of the second, it is difficult to assert that they can cover the entire spectrum of stability problems that arise in technology. The criterion of critical energy levels allows one to set and solve stability problems without restrictions on the smallness of displacements, the type of impact on the system, and is intended for formulating boundary states. To understand the essence of the mentioned criteria and to illustrate the differences, simple problems are proposed in the form of systems with lumped parameters with several degrees of freedom. The design research technique is illustrated by the example of a system model with lumped parameters in the form of elastic hinges. Energy relations are given that describe the state of the system at critical energy levels. The results obtained for critical internal forces coincide with the values of external critical loads known from the literature, which confirms the well-known fact of the theory of eigenvalue problems that the branch points of the solution coincide in linear and nonlinear formulations. A technique for determining the values of the deviation angles of the system elements in elastic hinges is shown. A comparison is made of the rotation angles of the system elements in the formulation of the problem in a linear (infinitely small deviation angles) and non-linear formulation.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124650071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.71.78
A. Marutyan
The article presents a new method of manufacturing lattices with faceless assemblies for truss structures made of profile pipes (bent-welded profiles), tested on their triangular and diagonal systems including flat and cross modifications. Its efficiency and rationality are shown in nodes where the belt elements of square pipes differ in a rhombic arrangement relative to the plane of the structure, which are more preferably replaced by triangular and pentagonal profiles. The versatility of the manufacturing method ensures its relevance in structures made of tubular and rolled profiles, preserves the accepted layout of standardized trusses with faceless assemblies and flange connections. The regularity of the optimization calculation of the unification zones in relation to the core elements of the lattices with the determination of their design coefficients is given. A comparative calculation of the design coefficients and the averaged coeffi cients of the use of the core elements of the grid of square and rectangular profiles is carried out on the example of their implementation in the same semi-truss, when the number of unification zones coincides. The noticeable reduction in the structural material (steel) and the lowering of the construction height of the truss structure were revealed. The acceptable correctness of the approximate calculation method for its application in solving optimization and variant problems, as well as at different stages of the design of load-bearing structures, is confirmed.
{"title":"Optimization of truss lattices from profile pipes (bent-welded profiles)","authors":"A. Marutyan","doi":"10.37538/0039-2383.2022.3.71.78","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.71.78","url":null,"abstract":"The article presents a new method of manufacturing lattices with faceless assemblies for truss structures made of profile pipes (bent-welded profiles), tested on their triangular and diagonal systems including flat and cross modifications. Its efficiency and rationality are shown in nodes where the belt elements of square pipes differ in a rhombic arrangement relative to the plane of the structure, which are more preferably replaced by triangular and pentagonal profiles. The versatility of the manufacturing method ensures its relevance in structures made of tubular and rolled profiles, preserves the accepted layout of standardized trusses with faceless assemblies and flange connections. The regularity of the optimization calculation of the unification zones in relation to the core elements of the lattices with the determination of their design coefficients is given. A comparative calculation of the design coefficients and the averaged coeffi cients of the use of the core elements of the grid of square and rectangular profiles is carried out on the example of their implementation in the same semi-truss, when the number of unification zones coincides. The noticeable reduction in the structural material (steel) and the lowering of the construction height of the truss structure were revealed. The acceptable correctness of the approximate calculation method for its application in solving optimization and variant problems, as well as at different stages of the design of load-bearing structures, is confirmed.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"193 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131650128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.2.8
I. Belutsky, I. V. Lazarev
The publication shows the importance of longitudinal reinforcement in terms of ensuring the crack resistance of the cross sections of the passage slab in reinforced concrete slabs of the roadway of composite reinforced concrete Superstructures Bridge. A calculation model is presented that allows determining the forces in the passage slab and an algorithm for determining the forces in the cross sections of the slab.
{"title":"Crack resistance and load-bearing capacity cross sections carriageway composite reinforced concrete superstructures bridge","authors":"I. Belutsky, I. V. Lazarev","doi":"10.37538/0039-2383.2022.3.2.8","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.2.8","url":null,"abstract":"The publication shows the importance of longitudinal reinforcement in terms of ensuring the crack resistance of the cross sections of the passage slab in reinforced concrete slabs of the roadway of composite reinforced concrete Superstructures Bridge. A calculation model is presented that allows determining the forces in the passage slab and an algorithm for determining the forces in the cross sections of the slab.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114983699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.49.54
S. Osykov, A. Trofimov
This paper presents an analytical expression for determining the friction capacity parameter in steel-concrete composites under bending moments. The analytical values of the deflections are compared with the values obtained experimentally. The results show that neglecting the interfacial effect in current standards and guidelines leads to incorrect assessment of structural deformability. The proposed analytical model can be used to determine the stiffness of steel-concrete composite slabs simply supported at both ends.
{"title":"Influence of interfacial interaction to the stiffness of steel-concrete composites under bending moments","authors":"S. Osykov, A. Trofimov","doi":"10.37538/0039-2383.2022.3.49.54","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.49.54","url":null,"abstract":"This paper presents an analytical expression for determining the friction capacity parameter in steel-concrete composites under bending moments. The analytical values of the deflections are compared with the values obtained experimentally. The results show that neglecting the interfacial effect in current standards and guidelines leads to incorrect assessment of structural deformability. The proposed analytical model can be used to determine the stiffness of steel-concrete composite slabs simply supported at both ends.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115782643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.28.34
A. Soloveva, A. Inkov, S. Solovev
The article describes a method for the reliability analysis of hinge-rod systems (trusses) with an interval estimation of the variability limits of random variables. In practical tasks of structural reliability analysis, it is often not possible to obtain complete statistical data that is necessary for a probabilistic and statistical approach in accordance with GOST 27751-2014. The use of alternative theories of data analysis makes it possible to obtain a define assessment of reliability with incomplete statistical data without introducing unconfirmed hypotheses about the form and shape of probability distribution functions of random variables. In this paper, it is proposed to use data on the limits of variability of random variables (an interval analysis) to assess the reliability of hinge-rod systems on the truss example. A comparative analysis of the truss reliability is given by two approaches (the classical probabilistic-statistical and the proposed interval approach). By the interval approach, the reliability of the truss is lower due to the fact that the interval estimation takes into account other possible distributions within a given interval that differ from the normal probability distribution. In the case when it is impossible to determine the type of probability distribution, but the limits of variability for random variables are known, the use of the presented method is a more cautious for the safety of truss operation.
{"title":"A method for structural reliability analysis of trusses with interval uncertainty of random variables","authors":"A. Soloveva, A. Inkov, S. Solovev","doi":"10.37538/0039-2383.2022.3.28.34","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.28.34","url":null,"abstract":"The article describes a method for the reliability analysis of hinge-rod systems (trusses) with an interval estimation of the variability limits of random variables. In practical tasks of structural reliability analysis, it is often not possible to obtain complete statistical data that is necessary for a probabilistic and statistical approach in accordance with GOST 27751-2014. The use of alternative theories of data analysis makes it possible to obtain a define assessment of reliability with incomplete statistical data without introducing unconfirmed hypotheses about the form and shape of probability distribution functions of random variables. In this paper, it is proposed to use data on the limits of variability of random variables (an interval analysis) to assess the reliability of hinge-rod systems on the truss example. A comparative analysis of the truss reliability is given by two approaches (the classical probabilistic-statistical and the proposed interval approach). By the interval approach, the reliability of the truss is lower due to the fact that the interval estimation takes into account other possible distributions within a given interval that differ from the normal probability distribution. In the case when it is impossible to determine the type of probability distribution, but the limits of variability for random variables are known, the use of the presented method is a more cautious for the safety of truss operation.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116763084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.61.70
S. V. Bakushev
We consider the generalized plane deformation of physically and geometrically nonlinear continuous medium. The mathematical model of medium is described by physically nonlinear relations in the form of arbitrary cross dependences between the first invariants of tensors and the second invariants of stress and strain deviators, taking into account geometrical nonlinearity (according to V.V. Novozhilov). The system of resolving partial differential equations of equilibrium, done in displacements, is quasilinear. This type is being investigated. Despite the fact that the type of the system of quasilinear partial differential equations in a certain part of space can be determined only for a specific solution, it is stated that in the general case the system of differential equations of equilibrium of generalized plane deformation is a system of mixed type. The type of the system of partial differential equations in a given area of space is completely determined by the values of its coefficients, and therefore depends both on the value of physical constants of continuous medium material and also on the value of derivatives of displacements in spatial coordinates.
{"title":"SOME ISSUES ON STATICS OF GEOMETRICALLY AND PHYSICALLY NONLINEAR CONTINUOUS MEDIUM","authors":"S. V. Bakushev","doi":"10.37538/0039-2383.2022.3.61.70","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.61.70","url":null,"abstract":"We consider the generalized plane deformation of physically and geometrically nonlinear continuous medium. The mathematical model of medium is described by physically nonlinear relations in the form of arbitrary cross dependences between the first invariants of tensors and the second invariants of stress and strain deviators, taking into account geometrical nonlinearity (according to V.V. Novozhilov). The system of resolving partial differential equations of equilibrium, done in displacements, is quasilinear. This type is being investigated. Despite the fact that the type of the system of quasilinear partial differential equations in a certain part of space can be determined only for a specific solution, it is stated that in the general case the system of differential equations of equilibrium of generalized plane deformation is a system of mixed type. The type of the system of partial differential equations in a given area of space is completely determined by the values of its coefficients, and therefore depends both on the value of physical constants of continuous medium material and also on the value of derivatives of displacements in spatial coordinates.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"16 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124191186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.37538/0039-2383.2022.3.18.27
E. Koreneva, V. Grosman
The analytical method for computation of circular thin combined plates with piecewise thickness subjected to an action of antisymmetric loads is proposed. The construction under study consists of several ring plates of variable thickness closely adjoining to each other. The laws of thickness variation of separate sections are different. The separate sections may be made from the same or from the different materials. These materials can be orthotropic or isotropic, inhomogeneous or homogeneous. In the places of separate parts conjugation the construction’s thickness may be continuous or discontinuous. For the analysis of antisymmetric flexure of the constructions under examination the theory of special functions is used. The solutions are obtained in closed form in terms of Legendre functions, Gegenbauer, Legendre and Lagerre polynomials. The conditions of separate parts conjugation are fulfilled. For this aim the special auxiliary functions are introduced.
{"title":"Combined constructions with piecewise thickness subjected to an action of unsymmetric loads","authors":"E. Koreneva, V. Grosman","doi":"10.37538/0039-2383.2022.3.18.27","DOIUrl":"https://doi.org/10.37538/0039-2383.2022.3.18.27","url":null,"abstract":"The analytical method for computation of circular thin combined plates with piecewise thickness subjected to an action of antisymmetric loads is proposed. The construction under study consists of several ring plates of variable thickness closely adjoining to each other. The laws of thickness variation of separate sections are different. The separate sections may be made from the same or from the different materials. These materials can be orthotropic or isotropic, inhomogeneous or homogeneous. In the places of separate parts conjugation the construction’s thickness may be continuous or discontinuous. For the analysis of antisymmetric flexure of the constructions under examination the theory of special functions is used. The solutions are obtained in closed form in terms of Legendre functions, Gegenbauer, Legendre and Lagerre polynomials. The conditions of separate parts conjugation are fulfilled. For this aim the special auxiliary functions are introduced.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114697240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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