On solving the plastoelastic problen in space of the commutative matrixes
A method for calculating mechanical parameters of multilayer structural elements (MSE) and their layers in elastic and plastoelastic zones are presented and grounded in the case of axial stretching. The method of diagonal matrices is proposed to define the parameters of MSE's and their layers...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2001-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/34638 |
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| _version_ | 1825197237999763456 |
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| author | Vytautas Kleiza |
| author_facet | Vytautas Kleiza |
| author_sort | Vytautas Kleiza |
| collection | DOAJ |
| description |
A method for calculating mechanical parameters of multilayer structural elements (MSE) and their layers in elastic and plastoelastic zones are presented and grounded in the case of axial stretching. The method of diagonal matrices is proposed to define the parameters of MSE's and their layers. In the elastic zone, MCE's are completely defined by two matrices: that of the modulus of elasticity and layer cross-section areas. In the plastoelastic zone, by the matrix of the layer crosssection areas and a diagonal matrix-function that defines σ - ε diagrams of the layers. In the case of stretching, the above mentioned matrices make up a commutative group with respect to product operation which makes it possible to obtain compact expressions for the required parameters that do not depend on the number of layers and are analogous to scalar ones (a single-layer case). This kind of calculation methods enables us to compute the values of axial stiffness and normal stress as well as the quantity of limiting axial load or the zones areas of elastic and plastoelastic deformation, when the diagrams σ - ε of deformation materials composing it correspond to that diagram that of plastoelastic and elastically-strengthening materials.
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| format | Article |
| id | doaj-art-4ff42bb5460c42109ec96aebd21d2c7c |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2001-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-4ff42bb5460c42109ec96aebd21d2c7c2025-02-11T18:14:13ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2001-12-0141spec.10.15388/LMR.2001.34638On solving the plastoelastic problen in space of the commutative matrixesVytautas Kleiza0Institute of Mathematics and Informatics A method for calculating mechanical parameters of multilayer structural elements (MSE) and their layers in elastic and plastoelastic zones are presented and grounded in the case of axial stretching. The method of diagonal matrices is proposed to define the parameters of MSE's and their layers. In the elastic zone, MCE's are completely defined by two matrices: that of the modulus of elasticity and layer cross-section areas. In the plastoelastic zone, by the matrix of the layer crosssection areas and a diagonal matrix-function that defines σ - ε diagrams of the layers. In the case of stretching, the above mentioned matrices make up a commutative group with respect to product operation which makes it possible to obtain compact expressions for the required parameters that do not depend on the number of layers and are analogous to scalar ones (a single-layer case). This kind of calculation methods enables us to compute the values of axial stiffness and normal stress as well as the quantity of limiting axial load or the zones areas of elastic and plastoelastic deformation, when the diagrams σ - ε of deformation materials composing it correspond to that diagram that of plastoelastic and elastically-strengthening materials. https://www.zurnalai.vu.lt/LMR/article/view/34638 |
| spellingShingle | Vytautas Kleiza On solving the plastoelastic problen in space of the commutative matrixes Lietuvos Matematikos Rinkinys |
| title | On solving the plastoelastic problen in space of the commutative matrixes |
| title_full | On solving the plastoelastic problen in space of the commutative matrixes |
| title_fullStr | On solving the plastoelastic problen in space of the commutative matrixes |
| title_full_unstemmed | On solving the plastoelastic problen in space of the commutative matrixes |
| title_short | On solving the plastoelastic problen in space of the commutative matrixes |
| title_sort | on solving the plastoelastic problen in space of the commutative matrixes |
| url | https://www.zurnalai.vu.lt/LMR/article/view/34638 |
| work_keys_str_mv | AT vytautaskleiza onsolvingtheplastoelasticprobleninspaceofthecommutativematrixes |