On the use of deep, shallow or flat shell finite elements for the analysis of thin shell structures

This paper is confined to the study of thin shells. The aim is to summarize the different theories used and to examine the assumptions upon which each of them is based. The intention is to show when it is more suitable to use a particular approximation and to indicate the errors it introduces. Beginning with the general deep shell theory, some simplifications are introduced to obtain the shallow shell theories. The special implications of this theory for the finite element method are also examined. Finally the particular case of flat elements is discussed

General treatment of essential boundary conditions in reduced order models for non-linear problems

Inhomogeneous essential boundary conditions must be carefully treated in the formulation of Reduced Order Models (ROMs) for non-linear problems. In order to investigate this issue, two methods are analysed: one in which the boundary conditions are imposed in an strong way, and a second one in which a weak imposition of boundary conditions is made. The ideas presented in this work apply to the big realm of a posteriori ROMs. Nevertheless, an a posteriori hyper-reduction method is specifically considered in order to deal with the cost associated to the non-linearity of the problems. Applications to nonlinear transient heat conduction problems with temperature dependent thermophysical properties and time dependent essential boundary conditions are studied. However, the strategies introduced in this work are of general application.Fil: Cosimo, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Cardona, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Idelsohn, Sergio Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina. Institució Catalana de Recerca i Estudis Avancats; España. International Center for Numerical Methods in Engineering; Españ

Towards a New Turbulence Model Based on Lagrangian Flows, Reduced Order Models, and Global-Local Approximations

Although the Navier-Stokes equations represent correctly both, laminar fluid flows as well as turbulent ones, the current power of the computers does not allow solving the latter without making empirical approximations that make the results are only predictable within the same margins from which the empirical approximation was realized. Taking into account that the vast majority of fluid flows that must be simulated by the industries are indeed of a turbulent nature, this makes it worthwhile to continue improving the models so that they fit more and more with the physicsmathematic equations. The current project in which we are working is in that sense. Based on previous work, we are proposing a new turbulence model that fits more with the physic and can be solved in one of the current computer. Always within the multi-scale models, in which all the turbulence model are based, the new idea consists in: a) treating the macro-scale with lagrangian particles, which convect and diffuse the turbulence; b) solving the micro-scale as a problem of unstable laminar fluid flow subjected to velocity gradients; c) applying a Reduction Order Model (ROM) to the micro-scale; d) going from the microscale to the macro-scale as in a Global-Local Model with a ROM.Publicado en: Mecánica Computacional, vol. XXXV, no 1.Facultad de Ingenierí

Towards a New Turbulence Model Based on Lagrangian Flows, Reduced Order Models, and Global-Local Approximations

Although the Navier-Stokes equations represent correctly both, laminar fluid flows as well as turbulent ones, the current power of the computers does not allow solving the latter without making empirical approximations that make the results are only predictable within the same margins from which the empirical approximation was realized. Taking into account that the vast majority of fluid flows that must be simulated by the industries are indeed of a turbulent nature, this makes it worthwhile to continue improving the models so that they fit more and more with the physicsmathematic equations. The current project in which we are working is in that sense. Based on previous work, we are proposing a new turbulence model that fits more with the physic and can be solved in one of the current computer. Always within the multi-scale models, in which all the turbulence model are based, the new idea consists in: a) treating the macro-scale with lagrangian particles, which convect and diffuse the turbulence; b) solving the micro-scale as a problem of unstable laminar fluid flow subjected to velocity gradients; c) applying a Reduction Order Model (ROM) to the micro-scale; d) going from the microscale to the macro-scale as in a Global-Local Model with a ROM.Publicado en: Mecánica Computacional, vol. XXXV, no 1.Facultad de Ingenierí

All-hexahedral element meshing: Generation of the dual mesh by recurrent subdivision

The domain geometry is defined by means of a closed all-quadrilateral mesh. The outer mesh imposes very strong restrictions on the possible connectivities between the inner hexahedral elements. Following the guidelines of the outer topology, the inner one is almost entirely defined. Several ways may be decided for certain configurations, some of them requiring special considerations in order to achieve a valid FEM mesh. The process is entirely performed by constructing the (graph theoretical) dual of the hexahedral mesh, this means no metric information is handled until the final (positioning and smoothing) steps. The essential steps of this scheme are described by means of examples

The challenge of mass conservation in the solution of free‐surface flows with the fractional‐step method: Problems and solutions

The purpose of this paper is to put in evidence that the fractional‐step method (FSM) used to solve the incompressible transient Euler and Navier–Stokes equations for free‐surface flows has a problem inherent to the method that may produce unacceptable variations of the domain volume. A simple modification of the free‐surface boundary term is introduced in order to reduce considerably the volume loss and preserve the computational advantages of the FSM

Refinamiento adaptativo sobre SUPG. Un elemento de interfase

En este trabajo presentamos una nueva forma de implementar la técnica SUPG usando una estrategia de refinamiento adaptativo. Nos hemos abocado al tratamiento de los nodos irregulares sobre mallas no uniformes. Presentamos un procedimiento para desarrollar un nuevo elemento para evitar oscilaciones en las direcciones longitudinal y transversal a la interfase de refinamiento. Este elemento especial se testea sobre ecuaciones escalares hiperbólicas. Se presentan comparaciones con la técnica standard y se sacan conclusiones sobre la mejora introducida.Peer Reviewe

All‐hexahedral element meshing: automatic elimination of self‐intersecting dual lines

There has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to define the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to first prevent or eliminate self‐intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied.&nbsp

A Fully Coupled Formulation For Incompressible Fluid-Elastic Structure-Interactions

We present a general formulation for analysis of fluid flows with structural interactions using the particle finite element method (PFEM). The fluids are fully coupled to the structures that can undergo highly non-linear response due to large deformations. The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes(particles) in both the fluid and the structure domains. A mesh connects the nodes defining the discretized domains where the governing equations, expressed in an integral form are solved as in the standard FEM. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluidstructure interaction problems including free-fluid-surfaces, breaking waves and fluid particle separation may be easily solved with this formulation are presented.Fil: Marti, Julio Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Idelsohn, Sergio Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Limache, Alejandro Cesar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

All‐hexahedral mesh smoothing with a node‐based measure of quality

This research work deals with the analysis and test of a normalized‐Jacobian metric used as a measure of the quality of all‐hexahedral meshes. Instead of element qualities, a measure of node quality was chosen. The chosen metric is a bound for deviation from orthogonality of faces and dihedral angles. We outline the main steps and algorithms of a program that is successful in improving the quality of initially invalid meshes to acceptable levels. For node movements, the program relies on a combination of gradient‐driven and simulated annealing techniques. Some examples of the results and speed are also shown