Nonlinear dynamic response of functionally graded material plates using a high‐order implicit algorithm. Issue 12 (26th July 2020)

• Record Type: Journal Article
• Authors: Bourihane, Oussama; Hilali, Youssef; Mhada, Khadija
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 100:Issue 12(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-07-26
• Subjects: finite element method -- functionally graded material plate -- implicit high‐order algorithm -- nonlinear dynamics -- vibration; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.202000087
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: In this paper, the forced nonlinear dynamic behavior of functionally graded material (FGM) plate under external dynamic loads is analyzed by means of a high‐order implicit algorithm. The model is developed using the third‐order shear deformation plate kinematics (TSDT). Unlike previous works, in this contribution, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite. To handle integrals in the case of inhomogeneous FGMs, the stress vector is split to four parts and it is written in dimensionless form. The resulting equations of motion are established using the Hamilton principle. Finite element discretization is adopted using a four‐node quadrilateral element with seven degrees of freedom per node. The resolution of the nonlinear equations is made by a high‐order implicit algorithm based on the asymptotic numerical method (ANM) techniques. Numerical comparisons of vibration natural frequencies and dynamic response of FGM plates under external loading with literature and laminate composite modeling results are presented to validate the accuracy and the performance of the proposed model. Abstract : In this paper, the forced nonlinear dynamic behavior of functionally graded material (FGM) plate under external dynamic loads is analyzed by means of a high‐order implicit algorithm. The model is developed using the third‐order shear deformation plate kinematics (TSDT). Unlike previous works, in this contribution, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite….