scholarly journals Hermite–Lagrangian finite element formulation to study functionally graded sandwich beams

2016 ◽  
Vol 140 ◽  
pp. 567-581 ◽  
Author(s):  
J. Yarasca ◽  
J.L. Mantari ◽  
R.A. Arciniega
Keyword(s):  
Finite Element ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Sandwich Beams ◽  
Lagrangian Finite Element

Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate

2017 ◽  
Vol 29 (7) ◽  
pp. 1430-1455 ◽  
Author(s):  
Vinyas Mahesh ◽  
Piyush J Sagar ◽  
Subhaschandra Kattimani
Keyword(s):  
Finite Element ◽  
Electric Fields ◽  
Elastic Plate ◽  
Coupling Effect ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Geometrical Parameters ◽  
Element Formulation ◽  
Elastic Plates

In this article, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has been investigated using finite element methods. The contribution of overall coupling effect as well as individual elastic, piezoelectric, piezomagnetic, and thermal phases toward the stiffness of magneto-electro-thermo-elastic plates is evaluated. A finite element formulation is derived using Hamilton’s principle and coupled constitutive equations of magneto-electro-thermo-elastic material. Based on the first-order shear deformation theory, kinematics relations are established and the corresponding finite element model is developed. Furthermore, the static studies of magneto-electro-elastic plate have been carried out by reducing the fully coupled finite element formulation to partially coupled state. Particular attention has been paid to investigate the influence of thermal fields, electric fields, and magnetic fields on the behavior of magneto-electro-elastic plate. In addition, the effect of pyrocoupling on the magneto-electro-elastic plate has also been studied. Furthermore, the effect of geometrical parameters such as aspect ratio, length-to-thickness ratio, stacking sequence, and boundary conditions is studied in detail. The investigation may contribute significantly in enhancing the performance and applicability of functionally graded magneto-electro-thermo-elastic structures in the field of sensors and actuators.

A Simple Total-Lagrangian Finite-Element Formulation for Nonlinear Behavior of Planar Beams

2018 ◽  
Author(s):  
Enrico Babilio ◽  
Stefano Lenci
Keyword(s):  
Finite Element ◽  
Theoretical Model ◽  
Finite Difference ◽  
Shear Angle ◽  
Difference Schemes ◽  
Finite Element Formulation ◽  
Finite Difference Schemes ◽  
Element Formulation ◽  
Beam Model ◽  
Lagrangian Finite Element

The present contribution reports some preliminary results obtained applying a simple finite element formulation, developed for discretizing the partial differential equations of motion of a novel beam model. The theoretical model we are dealing with is geometrically exact, with some peculiarities in comparison with other existing models. In order to study its behavior, some numerical investigations have already been performed through finite difference schemes and other methods and are reported in previous contributions. Those computations have enlightened that the model under analysis turns out to be quite hard to handle numerically, especially in dynamics. Hence, we developed ad hoc the total-lagrangian finite-element formulation we report here. The main differences between the theoretical model and its numerical formulation rely on the fact that in the latter the absolute value of the shear angle is assumed to remain much smaller than unity, and strains are piecewise constant along the beam. The first assumption, which actually simplifies equations, has been taken on the basis of results from previous integrations, mainly through finite difference schemes, which clearly showed that, while other strains can achieve large values in their range of admissibility, shear angle actually remains small. The second assumption led us to define a two-nodes constant-strain finite element, with a fast convergence, in terms of number of elements versus solution accuracy. Although, at the present stage of this ongoing research, we have only early results from finite elements, they appear encouraging and start to shed new light on the behavior of the beam model under analysis.

scholarly journals A component-free Lagrangian finite element formulation for large strain elastodynamics

2021 ◽  
Author(s):  
Miguel Martín Stickle ◽  
Miguel Molinos ◽  
Pedro Navas ◽  
Ángel Yagüe ◽  
Diego Manzanal ◽  
...  
Keyword(s):  
Finite Element ◽  
Weighting Function ◽  
Large Strain ◽  
Finite Element Formulation ◽  
Large Strains ◽  
Element Formulation ◽  
New Approach ◽  
Symmetric Structure ◽  
Lagrangian Finite Element ◽  
Solid Dynamics

AbstractStandard finite element formulation and implementation in solid dynamics at large strains usually relies upon and indicial-tensor Voigt notation to factorized the weighting functions and take advantage of the symmetric structure of the algebraic objects involved. In the present work, a novel component-free approach, where no reference to a basis, axes or components is made, implied or required, is adopted for the finite element formulation. Under this approach, the factorisation of the weighting function and also of the increment of the displacement field, can be performed by means of component-free operations avoiding both the use of any index notation and the subsequent reorganisation in matrix Voigt form. This new approach leads to a straightforward implementation of the formulation where only vectors and second order tensors in $${\mathbb {R}}^3$$ R 3 are required. The proposed formulation is as accurate as the standard Voigt based finite element method however is more efficient, concise, transparent and easy to implement.

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