Adaptive anisotropic mesh technique for coupled problems: application to welding simulation

International audienceA major problem arising in finite element analysis of coupled problems, such as welding for instance, is the control of the mesh, that is an appropriate mastering of the spatial discretization to get accurate results in a minimum computer time. The present anisotropic adaptation procedure is controlled by a directional error estimator based on local interpolation error and recovery of the second derivatives of different fields involved in the finite element calculation. Error indicators are derived to define an anisotropic mesh metric field, which is an input of the pre existing 3D remeshing procedure. The mesh metric consists of a combination of several metrics, each corresponding to the error estimation associated with a selected field of the solution produced (temperature, phase fraction, stress component). Mesh modifications are used to anisotropically and continuously adapt the mesh. We demonstrate the efficiency of the method by applying it to a coupled thermal-mechanical-metallurgical simulation of arc welding. We demonstrate that the use of an anisotropic adaptive finite element method can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with isotropic meshes

Development of an adaptive hp-version finite element method for computational optimal control

In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications

A comprehensive performance evaluation of different mobile manipulators used as displaceable 3D printers of building elements for the construction industry

The construction industry is currently technologically challenged to incorporate new developments for enhancing the process, such as the use of 3D printing for complex building structures,which is the aim of this brief. To do so, we show a systematic study regarding the usability and performance of mobile manipulators as displaceable 3D printing machinery in construction sites,with emphasis on the three main different existing mobile platforms: the car-like, the unicycleand the omnidirectional (mecanum wheeled), with an UR5 manipulator on them. To evaluate its performance, we propose the printing of the following building elements: helical, square, circular and mesh, with different sizes. As metrics, we consider the total control effort observed in the robots and the total tracking error associated with the energy consumed in the activity to get a more sustainable process. In addition, to further test our work, we constrained the robot workspace thus resemblingreal life construction sites. In general, the statistical results show that the omnidirectional platform presents the best results –lowest tracking error and lowest control effort– for circular, helicoidal and mesh building elements; and car-like platform shows the best results for square-like building element. Then,an innovative performance analysis is achieved for the printing of building elements, with a contribution to the reduction of energy consumptio

The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows

The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with residual minimization; it delivers computational efficency by a hyper-reduction procedure based on the `gappy POD' technique. Originally presented in Ref. [1], where it was applied to implicit nonlinear structural-dynamics models, this method is further developed here and applied to the solution of a benchmark turbulent viscous flow problem. To begin, this paper develops global state-space error bounds that justify the method's design and highlight its advantages in terms of minimizing components of these error bounds. Next, the paper introduces a `sample mesh' concept that enables a distributed, computationally efficient implementation of the GNAT method in finite-volume-based computational-fluid-dynamics (CFD) codes. The suitability of GNAT for parameterized problems is highlighted with the solution of an academic problem featuring moving discontinuities. Finally, the capability of this method to reduce by orders of magnitude the core-hours required for large-scale CFD computations, while preserving accuracy, is demonstrated with the simulation of turbulent flow over the Ahmed body. For an instance of this benchmark problem with over 17 million degrees of freedom, GNAT outperforms several other nonlinear model-reduction methods, reduces the required computational resources by more than two orders of magnitude, and delivers a solution that differs by less than 1% from its high-dimensional counterpart

Optimizing the remeshing procedure by computational cost estimation of adaptive fem technique

The objective of adaptive techniques is to obtain a mesh which is optimal in the sense that the computational costs involved are minimal under the constraint that the error in the finite element solution is acceptable within a certain limit. But adaptive FEM procedure imposes extra computational cost to the solution. If we repeat the adaptive process without any limit, it will reduce efficiency of remeshing procedure. Sometimes it is better to take an initial very fine mesh instead of multilevel mesh refinement. So it is needed to estimate the computational cost of adaptive finite element technique and compare it with the FEM computational cost. The remeshing procedure can be optimized by balancing these computational costs