Geometrically Nonlinear Analysis of Laminated Composite Plates
Apstrakt
Abstract. The low mass density and the high tensile strength, usually expressed through the specific modulus of elasticity and the specific strength, have made composite materials lighter and stronger compared with most traditional materials (such as steel, concrete, wood, etc.) and have increased their application not only for secondary, but during the last two decades also for primarily structural members in aerospace and automotive industry, ship building industry and bridge design. Although weight saving has eliminated constrain of slenderness and thickness and has made possible use of very thin plate elements, they have become susceptible to large deflections. In such cases, the geometry of structures is continually changing during the deformation and geometrically nonlinear analysis should be adopted. In this paper the geometrically nonlinear laminated plate finite element model is obtained using the principle of virtual displacement. With the layerwise displacement field of Redd...y [1], nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. The obtained displacement dependent secant stiffness matrix is utilized in Direct interation procedure for the numerical solution of nonlinear finite element equilibrium equations. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the previous paper [2].
Ključne reči:
von Karman nonlinearity / Layerwise plate theory / Composite plates / Finite element / MATLAB programIzvor:
Proceedings / The 3th International Congress of Serbian Society of Mechanics, 2011, 2011, 411-424Izdavač:
- Serbian Society of Mechanics, Belgrade
Finansiranje / projekti:
- Istraživanje stanja i metoda unapređenja građevinskih konstrukcija sa aspekta upotrebljivosti, nosivosti, ekonomičnosti i održavanja (RS-MESTD-Technological Development (TD or TR)-36048)
Kolekcije
Institucija/grupa
GraFarTY - CONF AU - Ćetković, Marina AU - Vuksanović, Đorđe PY - 2011 UR - https://grafar.grf.bg.ac.rs/handle/123456789/1904 AB - Abstract. The low mass density and the high tensile strength, usually expressed through the specific modulus of elasticity and the specific strength, have made composite materials lighter and stronger compared with most traditional materials (such as steel, concrete, wood, etc.) and have increased their application not only for secondary, but during the last two decades also for primarily structural members in aerospace and automotive industry, ship building industry and bridge design. Although weight saving has eliminated constrain of slenderness and thickness and has made possible use of very thin plate elements, they have become susceptible to large deflections. In such cases, the geometry of structures is continually changing during the deformation and geometrically nonlinear analysis should be adopted. In this paper the geometrically nonlinear laminated plate finite element model is obtained using the principle of virtual displacement. With the layerwise displacement field of Reddy [1], nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. The obtained displacement dependent secant stiffness matrix is utilized in Direct interation procedure for the numerical solution of nonlinear finite element equilibrium equations. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the previous paper [2]. PB - Serbian Society of Mechanics, Belgrade C3 - Proceedings / The 3th International Congress of Serbian Society of Mechanics, 2011 T1 - Geometrically Nonlinear Analysis of Laminated Composite Plates EP - 424 SP - 411 UR - https://hdl.handle.net/21.15107/rcub_grafar_1904 ER -
@conference{ author = "Ćetković, Marina and Vuksanović, Đorđe", year = "2011", abstract = "Abstract. The low mass density and the high tensile strength, usually expressed through the specific modulus of elasticity and the specific strength, have made composite materials lighter and stronger compared with most traditional materials (such as steel, concrete, wood, etc.) and have increased their application not only for secondary, but during the last two decades also for primarily structural members in aerospace and automotive industry, ship building industry and bridge design. Although weight saving has eliminated constrain of slenderness and thickness and has made possible use of very thin plate elements, they have become susceptible to large deflections. In such cases, the geometry of structures is continually changing during the deformation and geometrically nonlinear analysis should be adopted. In this paper the geometrically nonlinear laminated plate finite element model is obtained using the principle of virtual displacement. With the layerwise displacement field of Reddy [1], nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. The obtained displacement dependent secant stiffness matrix is utilized in Direct interation procedure for the numerical solution of nonlinear finite element equilibrium equations. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the previous paper [2].", publisher = "Serbian Society of Mechanics, Belgrade", journal = "Proceedings / The 3th International Congress of Serbian Society of Mechanics, 2011", title = "Geometrically Nonlinear Analysis of Laminated Composite Plates", pages = "424-411", url = "https://hdl.handle.net/21.15107/rcub_grafar_1904" }
Ćetković, M.,& Vuksanović, Đ.. (2011). Geometrically Nonlinear Analysis of Laminated Composite Plates. in Proceedings / The 3th International Congress of Serbian Society of Mechanics, 2011 Serbian Society of Mechanics, Belgrade., 411-424. https://hdl.handle.net/21.15107/rcub_grafar_1904
Ćetković M, Vuksanović Đ. Geometrically Nonlinear Analysis of Laminated Composite Plates. in Proceedings / The 3th International Congress of Serbian Society of Mechanics, 2011. 2011;:411-424. https://hdl.handle.net/21.15107/rcub_grafar_1904 .
Ćetković, Marina, Vuksanović, Đorđe, "Geometrically Nonlinear Analysis of Laminated Composite Plates" in Proceedings / The 3th International Congress of Serbian Society of Mechanics, 2011 (2011):411-424, https://hdl.handle.net/21.15107/rcub_grafar_1904 .