The Node Dependent Kinematic form of Finite Element Method

Erasmo Carrera

Politecnico di Torino

Current Finite Elements implementation, including those in commercial software, are characterized by a fixed/limited number of degree of freedom per nodes. Normally these are ‘six’ for structural elements and ‘three’ for 3D ones. These constraints could lead to severe limitations to solve ‘localized’ stresses/fields, laminated composite and/or metallic structures, electromechanical problems and structures subjected to multifield loadings.

In recent years, the speaker and co-workers have developed a version of finite elements in which the number of degrees of freedom in the node can vary within the element, from node to node: this is the NDK, Node Dependent Kinematic version of FE. In other words, each node can refer to a different structural theory and the FEM matrices are weighted not only with respect to classical shape functions but also with respect to structural theory. This was done for one-dimensional, two-dimensional plane and curved and three-dimensional elements. The key tool for the generation of the NDK formulation is the Carrera Unified Formulation, proposed by the speaker more than 25 years ago, which allows the writing of stiffness matrices in terms of a few fundamental 'nuclei' that are essentially independent of the type of structural theory and shape functions used in the node.

This lecture illustrates the NDK FEM method and propose applications to various linear and non-linear, static and dynamic problems, metallic and laminated composite materials, mechanical and electrical loadings. In particular, the possibility of applying NDK to global-local problems without the need to use transition elements and/or penalty procedures will be highlighted. The advantage in terms of both accuracy and computational cost reduction of the NDK-FEM method over traditional FEM will be clearly shown. As approximating functions for the structural part, reference will be made to polynomial (Taylor-based) expansions, use of Lagrange and Legendre polynomials or a combination of these.

Biography

Dr Erasmo Carrera is Professor of Aeronautics and Astronautics at Politecnico di Torino. He acts as President of the Italian Association of Aeronautics and Astronautics, A.I.D.A.A, member of Accademia delle Scienze di Torino and Academie de l’Air et de l’Espace He has been visiting professor at the University of Stuttgart, Virginia Tech, Royal Melbourne Institute of Technology, Tambov University, Supmeca and Ensam, PMU. Dr Carrera has been responsible for various research contracts granted by public and private national and international institutions, including the European Community, European Space Agency, Thales Alenia Space and Embraer. He is founder and Editor-in-Chief of Advances in Aircraft and Spacecraft Science, Editor-in-Chief of Mechanics of Advanced Materials Structures and Section Editor of Journal and Sound and Vibration.

He has introduced the Unified Formulation, or CUF (Carrera Unifed Formulation), as a tool to establish a new framework in which to develop theories of beams, plates and shells for metallic and composite multilayered structures. He has been author and co-author of about 800 papers on the above topics. Carrera has been recipient of various 'best paper award' and of the 'JN Reddy Medal'. Professor Carrera has been Highly Cited Researchers (Top 100 Scientist) by Thompson Reuters in the two Sections: Engineering and Materials. He has been confirmed HiCI in 2015 in the Section Engineering. The only aerospace Engineering worldwide. Due to his scientific outcoming professor Carrera has been awarded by the President of Italian Republic, as 'Honoray Commendator'.