Maurice Touratier

A C1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A new three-noded C1 beam finite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three-dimensional elasticity solution is used in the present model. Since the field consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms. Performance of the element is tested by comparing the present results with exact three-dimensional solu-tions available for laminates under bending, and the elasticity three-dimensional solution deduced from the de Saint-Venant solution including both torsion with warping and bending. In addition, three-dimensional solid finite elements using 27 noded-brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the effects of various parameters such as length-to-thickness ratio, shear modular ratio, boundary conditions, free (de Saint-Venant) and constrained torsion. Copyright

A numerical simulation of steady state metal cutting

Abstract An arbitrary Lagrangian-Eulerian (ALE) approach is used to model the orthogonal metal cutting in a steady state situation. The thermomechanical model includes the effects of elasticity, plasticity, strain rate, large strains and friction with heat generated between the tool and the chip. The ALE formulation can combine the advantages of both the Eulerian and Lagrangian approaches in a single description. Particularly, problems linked to the free surface in a Eulerian description and those linked to severe mesh distortions in a Lagrangian one can be solved by this formulation. The ALE governing equations are briefly reviewed in this paper; finite element and finite volume methods are used for the discretization of the conservation equations and an explicit time integration is adopted. Only the steady state solution is required; the ALE formulation is exploited to update the free and the contact surfaces. The model predicts the thermomechanical quantities, the chip geometry and the cutting forces from the cutting data and the material and friction parameters. Cutting experiments were performed with 42CD4 steel and comparisons of experimental tool forces and chip geometry with the numerical results are presented.

Optimal design for minimum weight in a cracked pressure vessel of a turboshaft

The authors study the shape optimization of a complex cracked shell under complex criteria. The shell is one of various cases of a turboshaft, and optimization criteria are associated to the cost, the technology, and above all the working conditions for the turboshaft. The optimization criteria involved are of course the weight of the structure, but also the plastic instability and critical stress intensity factor. All computations have been made with the Ansys finite element program in which an optimization module exists.

Multilayered Piezoelectric Refined Plate Theory

A two-dimensional theory for the analysis of multilayered piezoelectric plates is presented. The theory is based on a hybrid approach in which the continuity conditions for both mechanical and electric unknowns at layer interfaces, as well as the imposed conditions on the bounding surfaces and at the interfaces, are independently satisfied. Then, the piezoelectric boundary-value problem is stated using mechanical displacements and electrostatic potential, in conjunction with the coupled piezoelectric constitutive law. The proposed model is simple to use, incorporating only five independent generalized displacements and one or two independent generalized electrostatic potentials as unknowns. The number of electric unknowns depends on the number of layers and electric prescribed conditions. The accuracy of the proposed theory is assessed through investigation of significant problems, for which an exact three-dimensional solution is known from Heyliger: first, in dynamics, the free vibrations of five-layered piezoelectric plates and second, in statics, for three-layered plates with an imposed force density. Results obtained with our model compare very well with the exact three-dimensional theory.

Torsional Vibration and Damping Analysis of Sandwich Beams

The objective of the paper presented here is to investigate the torsional vibration and damping analysis of beams with sandwich or constrained layer damping arrangements using finite element procedure. Finite element based on a sandwich beam theory, which satisfies the interface stress and displacement continuity and has zero shear stress on the top and bottom surfaces of the beam, is employed. The element is capable of simulating free as well as constrained torsion. The transverse shear deformation in the form of trigonometric sine function is incorporated to define the transverse shear strain. The inertia effects due to in-plane, rotary and torsional motion have been included in the formulation. The governing equations of motion for the dynamic analysis are obtained using Lagranges equation of motion. The solutions are evaluated by QR algorithm. Numerical results are presented for both free-free and cantilever beams. A detailed parametric study is carried out to highlight the influence of shear modulus of the core or constrained layer in beams, thickness ratio, and boundary condition on the torsional resonance frequencies and its associated system loss factors.

Refined finite element for piezoelectric laminated composite beams

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Computations of an engine to analyze cylinder distortion

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Shape optimization of a pressure vessel under plastic flow, plastic instability, weight and fatigue life criteria

finite element is formulated for analyzing the bending/torsional behavior of rectangular piezoelectric laminated composite beams. The formulation includes transverse shear, warping due to torsion and electro-elastic coupling effects. The shear strain is represented by a cosine function of a higher order in nature, thus avoiding shear correction factors. The warping function obtained from a three-dimensional elasticity solution is incorporated in the present model. The distribution of the electric potential through the thickness is accounted for in the formulation based on the observation of the three-dimensional solution. The efficacy of the laminated piezoelectric composite element is tested comparing the results with those of analytical and three-dimensional finite element models.

Modelling of Cutting and Machining: 10 years of ESAFORM activity

The aim of the research work presented here is to control the geometric distortions of engine cylinders, which involve both noise and oil consumption. The final goal is then to limit pollution from engines. The simulation deals initially with the cold stamping and crushing operations of a cylinder head gasket; based on using solid finite element models from the Abaqus computer code (version 5.3) for large deformation with plasticity and contact, including friction. In addition, experiments have been carried out to identify the plasticity rule for the materials used in order to simulate the crushing of the cylinder head gasket under a given normal pressure representing the clamping operation. The main difficulty of this work is to correlate the cylinder head gasket behaviour and cylinder distortions with the main function of the gasket, i.e. pressurized gas sealing. The cylinder head gasket is a complex multilayered structure made of three spot welded metal sheets. This assembly has many holes of different shapes. Around the cylinder hole on both outer layers of the gasket, there is a small size embossment to ensure gas sealing between the engine block and cylinder head. This rib is not circular because of the combustion chamber shape.

A C0 eight node finite element based on a shell theory

Abstract The structural shape optimization of a complex shell under complex criteria is presented. The shell is one of various cases of a turboshaft, and optimization criteria are associated with the cost, the technology, and above all the working conditions for the turboshaft. Optimization criteria involved are of course the weight of the structure, but also the plastic flow, plastic instability and fatigue life. The fatigue life criterion is an extension to the three-dimensional state of the one-dimensional Lemaitre-Chaboche rule, taking into account the elasto-plastic Neuber correction. All computations have been made with the ANSYS finite element program in which an optimization module exists.