Paulo M. Pimenta

Thermomechanical response of solids at high strains—Natural approach

Abstract The paper develops in pursuance of [4]the theoretical framework appertaining to coupled thermomechanical deformations of solids, subject to large as well as inelastic deformations. The essential feature of the analysis is a consistent natural formulation which encompasses also all thermodynamic aspects. On the other hand, it must be admitted that current concepts on mechanical constitutive assumptions [5, 6]are not sufficiently sophisticated to permit a precise generalisation for the purpose of incorporating thermomechanical effects and delivering a fully compatible theory of the coupled problem. Uniqueness and bifurcation of the solutions as well as stable postcritical deformation paths are also considered in this account. Furthermore, algorithms for the solution of the nonlinear algebraic equations representing the discretised problem and, in particular, quasi-Newton techniques are discussed. The paper concludes with a number of applications of technical relevance.

Natural finite element techniques for viscous fluid motion

Abstract The paper surveys recent work on fluid dynamics performed at the ISD, University of Stuttgart. It is in particular directed to a natural description of the flow phenomena and includes also a consideration of thermally coupled problems. The derivation of the relevant finite element equations when referred to natural quantities is outlined and examples of application are given. Also presented is a discussion on the associated modern developments in numerical solutions techniques.

New trends in thin structures : formulation, optimization and coupled problems

A plate theory as a mean to compute precise 3D-solutions including edge effects and related (O. Allix and C. Dupleix-Courdec) A fully nonlinear thin shell model of Kirchhoff-Love type (P.M. Pimenta, E.S. Almeida Neto and E.M.B. Campello) A beam finite element for nonlinear analysis of shape memory alloy devices (E. Artioli, F. Auricchio and R.L. Taylor) A unified approach for the nonlinear dynamics of rods and shells using an exact conserving integration algorithm (P.M. Pimenta and E.M.B. Campello) Advanced Numerical Methods for the Form Finding and Patterning of Membrane Structures (K.-U. Bletzinger, J. Linhard and R. Wuechner) Contact between beams and shells (P. Wriggers) Advances in computational fluid-thin-walled-structure interaction-formulations and solvers (W.A. Wall, U. Kuettler, A. Gerstenberger, M. Gee and Ch. Foerster) Advances in Subdivision Finite Elements for Thin Shells (F. Cirak and Q. Long)

A Fully Nonlinear Thin Shell Model of Kirchhoff-Love Type

This work presents a fully nonlinear Kirchhoff-Love shell model. In contrast with shear flexible models, our approach is based on the Kirchhoff-Love theory for thin shells, so that transversal shear deformation is not accounted for.

Loop Formation in Catenary Risers on Installation Conditions: A Comparison of Statics and Dynamics

Loop formation may occur in cables, ropes, and also risers — flexible pipes or umbilical cables — used for offshore exploitation. The phenomenon occurs when there is enough torsion moment in the line and also a low tension condition or, even in the cases of cable slack (almost zero tension) with some torsion moment. Many references discuss about the loop formation prediction in different conditions, but mostly for the cases of an initial straight cable (rope or riser) which is usually represented by a beam. The problem of the loop formation in a catenary riser including the nonlinear contact with the seabed is very important, once during the riser installation in some conditions a low tension combined with torsion moment can lead to the loop formation, which is undesirable. There is a necessity of a better understanding of this theme. The present work explores the loop formation in catenary risers comparing the results of the static and the dynamic predictions, showing an asymptotic tendency from the dynamics to the statics. For that study, geometrically-exact nonlinear beam models were employed in the statics and in dynamics, leading to very realistic loop formation predictions.Copyright

Finite Element analysis of the wrinkling of orthotropic membranes

This work presents a fully nonlinear formulation for the analysis of the wrinkling on orthotropic membranes. Our approach describes the membrane kinematics as a thin shell motion, whose bending stiffness comes naturally from the shell assumptions. We combine the geometrically-exact isotropic shell model of [1],[2] with an orthotropic constitutive equation for the membrane strains (see [3],[4]), so that both bending and typical membrane capabilities are present in a totally consistent way. The strain energy function is split into an isotropic and an orthotropic part, the first one being relative to the shell (hyperelastic) behavior and the latter to the membrane deformations. The model is discretized under the light of the finite element method using the six-node triangular element of [2], and the performance of the formulation is assessed in several numerical examples (see e.g. Fig. 1). Unstructured meshes are deliberately employed whereas small geometrical imperfections are imposed for the wrinkles to be initiated. Experimental data from the membrane tests of [5] are also taken into account for comparison with our results. Open image in new window Fig. 1 Stretching of two orthotrophic membranes. Deformed configurations.

Hydrostatic Pressure Load in Pipes Modeled Using Beam Finite Elements: Theoretical Discussions and Applications

AbstractThis work presents a derivation of equivalent loads, coming from the integration of hydrostatic pressure fields on the internal and external walls of a curved pipe, which is modeled as a Eu...

Elastic-plastic analysis of metallic shells at finite strains

The geometrically-exact finite-strain variable-thickness shell model of [1] is reviewed in this paper and extended to the case of metallic elastoplastic shells. Isotropic elasticity and von Mises yield criterion with isotropic hardening are considered. The model is implemented within a triangular finite element and is briefly assessed by means of two numerical examples.

A 3D study of the contact interface behavior using elastic-plastic constitutive equations

In this work a homogenization method presented by Bandeira et al [2,3,4] is enhanced in order to obtain by numerical simulation the interface law for the normal contact pressure based on statistical surface models. For this purpose elasticplastic behavior of the asperities is considered. Statistical evaluations of numerical simulations lead to a constitutive law for the contact pressure. The resulting law compared with other laws stemming from analytical investigations, like those presented by Greenwood Williamson [11] and Yovanovich [19, 32]. The non-penetration condition and the interface model for contact that takes into account the surface microstructure are investigated in detail. This paper can be regarded as a complementary study to that presented by Bandeira et al [2]. Here the plasticity of the asperities is taken into account by assuming a constitutive equation based on an associated von Mises yield function formulated in principal axes, as shown by Pimenta [22]. The basic aim of this paper is to derive constitutive contact laws for a rough surface by using the finite element method. For this purpose one has to model and discretize the rough surface and then, by homogenization procedures develop an interface law for contact. The interface law is obtained from numerical simulation using a model that consists of two deformable bodies in contact. The contact surfaces of both bodies are rough. The law obtained by numerical simulations and statistical evaluation of the numerical results is compared with analytically derived laws that regard plasticity. An augmented Lagrangian method is applied to solve the contact problem, see Bertsekas [5,6], Fletcher [10], Luenberger [18], Laursen, Maker [15], Laursen, Simo [16, 17], Wriggers [27], Wriggers, Simo [28], Wriggers et al. [29], Wriggers, Zavarise [31] and Heegaard, Curnier [12]. The technique used to solve threedimensional contact problems with friction, see Curnier [7] and Tabor [26], in finite deformations was 314 A.A. Bandeira, P.M. Pimenta, and P. Wriggers already developed and described in Bandeira et al [2,3,4], Simo, Laursen [24], Wriggers [27, 28, 29, 30, 31], Alart, Curnier [1] and Oden, Pires [20]. Numerical examples are selected to show the ability of the algorithm to represent interface law for rough surfaces considering elastoplastic behaviour of the asperities.

Hybrid and Mixed Variational Principles for the Geometrically Exact Analysis of Shells

This paper addresses the development of some alternative hybrid and mixed variational formulations for the geometrically-exact three-dimensional first-order-shear shell boundary value problem. In the framework of the complementary-energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of the cross-sectional resultants only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value-problem. The main features of the principles are highlighted, giving special attention to their relationships from both theoretical and numerical point of view.