Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric Loading
Depending on the load level, structures can experience a material nonlinearity known as elastoplasticity, which has an important role in the behaviour of structures. In order to avoid the elastoplastic behaviour, it is necessary to find the optimal thickness distribution, which corresponds to the mi...
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MDPI AG
2023-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/9/5325 |
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| author | José Simões Moita Aurélio Lima Araújo Victor Franco Correia Cristóvão Mota Soares José Herskovits |
| author_facet | José Simões Moita Aurélio Lima Araújo Victor Franco Correia Cristóvão Mota Soares José Herskovits |
| author_sort | José Simões Moita |
| collection | DOAJ |
| description | Depending on the load level, structures can experience a material nonlinearity known as elastoplasticity, which has an important role in the behaviour of structures. In order to avoid the elastoplastic behaviour, it is necessary to find the optimal thickness distribution, which corresponds to the minimum mass that provides an elastic behaviour for a certain load level. The elastoplasticity analysis of functionally graded axisymmetric shells under axisymmetric mechanical loading, and the subsequent optimization, was performed by using a simple conical frustum finite element model with two nodal circles; three degrees of freedom per node, which was based on Kirchhoff’s theory allowing for shear deformation; and using a reduced numerical integration procedure that is essential for its success when applied to thin shells. The formulation accounts for the calculation of the displacements and through-thickness stress distribution, including the effective stress. In this work, the thickness was the design variable in the optimization procedure and the mass was the objective function that needed to be minimized subject to a constraint imposed on the effective stress. The optimization solutions were obtained by using a feasible arc interior point gradient-based algorithm. Some illustrative examples were performed, and the corresponding results are presented and discussed. |
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| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T04:24:09Z |
| publishDate | 2023-04-01 |
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| spelling | doaj.art-565baa73dd7741a7b1f3eab82cd4c01f2023-11-17T22:32:27ZengMDPI AGApplied Sciences2076-34172023-04-01139532510.3390/app13095325Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric LoadingJosé Simões Moita0Aurélio Lima Araújo1Victor Franco Correia2Cristóvão Mota Soares3José Herskovits4IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, PortugalIDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, PortugalEscola Superior Náutica Infante D. Henrique, Av. Eng. Bonneville Franco, 2770-058 Paço de Arcos, PortugalIDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, PortugalCOPPE/UFRJ, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-909, BrazilDepending on the load level, structures can experience a material nonlinearity known as elastoplasticity, which has an important role in the behaviour of structures. In order to avoid the elastoplastic behaviour, it is necessary to find the optimal thickness distribution, which corresponds to the minimum mass that provides an elastic behaviour for a certain load level. The elastoplasticity analysis of functionally graded axisymmetric shells under axisymmetric mechanical loading, and the subsequent optimization, was performed by using a simple conical frustum finite element model with two nodal circles; three degrees of freedom per node, which was based on Kirchhoff’s theory allowing for shear deformation; and using a reduced numerical integration procedure that is essential for its success when applied to thin shells. The formulation accounts for the calculation of the displacements and through-thickness stress distribution, including the effective stress. In this work, the thickness was the design variable in the optimization procedure and the mass was the objective function that needed to be minimized subject to a constraint imposed on the effective stress. The optimization solutions were obtained by using a feasible arc interior point gradient-based algorithm. Some illustrative examples were performed, and the corresponding results are presented and discussed.https://www.mdpi.com/2076-3417/13/9/5325functionally graded materialfinite element methodoptimization |
| spellingShingle | José Simões Moita Aurélio Lima Araújo Victor Franco Correia Cristóvão Mota Soares José Herskovits Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric Loading Applied Sciences functionally graded material finite element method optimization |
| title | Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric Loading |
| title_full | Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric Loading |
| title_fullStr | Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric Loading |
| title_full_unstemmed | Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric Loading |
| title_short | Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric Loading |
| title_sort | optimization on elastoplasticity of functionally graded shells of revolution under axisymmetric loading |
| topic | functionally graded material finite element method optimization |
| url | https://www.mdpi.com/2076-3417/13/9/5325 |
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