Variational-asymptotic method and application to smart and functionally graded structures

Le, Khanh Chau

Institute for Computational Science, Ton Duc Thang University

Institute of Mechanics of Materials, Ruhr University Bochum, Germany



The variational-asymptotic method is a universal method applicable to all variational problems with a small parameter. It can be applied to the problem of dimension reduction for intelligent and functionally graded structures. In this talk, an asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived from the three-dimensional theory of piezoelectricity using this method. The error estimate of the constructed theory is given in the energetic norm. As an application, an analytical solution is found for the problem of forced vibration of a functionally graded piezoceramic cylindrical shell with thickness polarization, completely covered by electrodes and excited by a harmonic voltage. Another analytical solution is found for the problem of forced vibration of a circular elastic plate partially covered by two piezoceramic patches with thickness polarization. We also discuss the problem of a mems sensor bonded to an elastic plate and derive the equation of motion for this sandwich structure by the variational-asymptotic method. A finite element method is developed to solve this problem.

Le, Khanh Chau

Biography (Khanh Chau Le)

Khanh Chau Le is a senior researcher at Ton Duc Thang University (Ho Chi Minh City, Vietnam). Until 2021 he was a professor of mechanics at the Ruhr University Bochum. From 2009 until 2017 he was a flying faculty member and Co-Director of the Master Program in Computational Engineering at the Vietnamese German University. From 2018 until 2021 he was a professor and a head of the Materials Mechanics Research Group at the Ton Duc Thang University (Ho Chi Minh City, Vietnam). He was a visiting professor at Ecole Polytechnique (Palaiseau, France) and spent several research stays at Wayne State University (Detroit, USA). He is an associate editor of Vietnam Journal of Mechanics and a member of editorial boards of three international journals in mechanics (International Journal of Plasticity, Archive of Applied Mechanics, and Symmetry). He serves as a reviewer of various international journals. He is the scientific supervisor of 11 PhD students and 48 Master students.

His first scientific results relate to applications of the variational-asymptotic method in the theory of low- and high-frequency vibrations of elastic shells, plates, and rods. He developed also the theories of low- and high-frequency vibrations of piezoelectric shells, plates, and rods. Variational-asymptotic method and its applications in the theory of vibrations of shells, plates, and rods was summarized in his monograph “Vibrations of shells and rods”, Berlin, Springer Verlag, 1999. He is the author of two other books entitled "Introduction to Micromechanics" (first and second editions) and "Energy Methods in Dynamics" (first and second editions).
Dr. Le’s recent research interests are in the field of dynamics of smart and functionally graded structures, nonlinear vibration and wave propagation, fracture mechanics, crystal plasticity, micromechanics, and thermodynamic dislocation theory. His results in these areas are presented in leading scientific journals and at various conferences (about 120 publications).


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