Automatic finite element formulation and assembly of hyperelastic higher order structural models

Ramabathiran, Amuthan Arunkumar ; Gopalakrishnan, S. (2014) Automatic finite element formulation and assembly of hyperelastic higher order structural models Applied Mathematical Modelling, 38 (11-12). pp. 2867-2883. ISSN 0307-904X

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The formulation of higher order structural models and their discretization using the finite element method is difficult owing to their complexity, especially in the presence of nonlinearities. In this work a new algorithm for automating the formulation and assembly of hyperelastic higher-order structural finite elements is developed. A hierarchic series of kinematic models is proposed for modeling structures with special geometries and the algorithm is formulated to automate the study of this class of higher order structural models. The algorithm developed in this work sidesteps the need for an explicit derivation of the governing equations for the individual kinematic modes. Using a novel procedure involving a nodal degree-of-freedom based automatic assembly algorithm, automatic differentiation and higher dimensional quadrature, the relevant finite element matrices are directly computed from the variational statement of elasticity and the higher order kinematic model. Another significant feature of the proposed algorithm is that natural boundary conditions are implicitly handled for arbitrary higher order kinematic models. The validity algorithm is illustrated with examples involving linear elasticity and hyperelasticity.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Hyperelasticity; Geometric Nonlinearity; Automatic Finite Element Formulation; Automatic Finite Element Assembly; Automatic Differentiation; Higher Order Structural Model
ID Code:99057
Deposited On:03 Sep 2015 06:08
Last Modified:03 Sep 2015 06:08

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