Coupled euler lagrangian approach using abaqusexplicit in the bird strike aircraft damage analysis i. Lagrangian formulation thats the energy formulation now onto the lagrangian formulation. Updated lagrangian formulation for incremental general nonlinear analysis principle of virtual work in terms of 2nd piolakirchhoff stresses and greenlagrange strains referred to the configuration at time t. These approaches are distinguished by three important aspects. Ale methods use a generalized formulation and capture the advantages of.
The finite element method for the analysis of nonlinear and dynamic systems prof. The finite element method for the analysis of nonlinear. Adaptive meshing and distortion control imechanica. Arbitrary lagrangianeulerian finite element formulations applied. Lagrangian elements are always 100% full of a single material, so the material boundary coincides with an element boundary. How to model eulerian regions in a coupled eulerian. Incremental stress and strain decompositions in the updated lagrangian form of the principle of virtual work. Adaptive meshing in abaqus explicit is intended to model largedeformation problems. Advantages of arbitrary lagrangian eulerian finite element techniques the arbitrary lagrangian eulerian ale is a finite element formulation in which the computational system is not a prior fixed in space e. At this point it seems to be personal preference, and all academic, whether you use the lagrangian method or the f ma method.
The lagrangian formulation, in contrast, is independent of the coordinates, and the equations of motion for a noncartesian coordinate system can typically be found immediately using it. Coupled euler lagrangian approach using abaqus explicit in the bird strike aircraft damage analysis 1. Then he told me something i have always found fascinating. Abaqus users question about geometric nonlinearity. Principle of virtual work in terms of 2nd piolakirchhoff stresses and greenlagrange strains referred to the configuration at time t.
Before in tro ducing lagrangian mec hanics, lets dev elop some mathematics w e will need. The scheme is lagrangian and hamiltonian mechanics. This paper presents the steps to achieve a fe model of the fsw process in the abaqus explicit software, using the coupled eulerian lagrangian formulation cel, the johnsoncook constitutive. The lagrangian formalism when i was in high school, my physics teacher called me down one day after class and said, you look bored, i want to tell you something interesting. In general, the safest method for solving a problem is to use the lagrangian method and then doublecheck things with f ma andor. Lagrangian mechanics applies to the dynamics of particles, while fields are described using a lagrangian density. I tried to search its documentation, but didnt find any relevant information. Simulation of end milling on fem using ale formulation.
The coupled eulerian lagrangian cel approach in abaqus which provides engineers and scientists with the ability to simulate a class of problems where the interaction between structures and fluids is important. Advantages of arbitrary lagrangianeulerian finite element techniques the arbitrary lagrangianeulerian ale is a finite element formulation in which the computational system is not a prior fixed in space e. Some models parts tools are described by updated lagrangian formulation, other parts material are described. Lagrangian mechanics is widely used to solve mechanical problems in physics and when newtons formulation of classical mechanics is not convenient. First that we should try to express the state of the mechanical system using the minimum representation possible and which re ects the fact that the physics of the problem is coordinateinvariant.
Pdf application of the coupled eulerianlagrangian cel. This expression is written in abaqus theory manual as. Lagrangian formulation was used by most of the researchers, except strenkowski, moon, and athavale 5, 6 that prefer to use the eulerian. Abaqus explicit arbitrary lagrangian eulerian formulation ale. Just for comparison, lsdyna, another fe software package, does report lagrangian strain. The abaqus documentation often refers to ale adaptive meshing simply as adaptive meshing. This new modelling technique enables better capturing of fluidlike bird behaviour upon impact in the velocity range at which bird strikes usually occur. Lagrangian and hamiltonian mechanics a short introduction. Coupled euler lagrangian approach using abaqus explicit. As a preliminary analysis perform free vibration analysis to obtain 30 vibration modes and their natural frequencies.
It is more suitable for fluid flow problems, which involves a control volume. The adaptive meshing implementation in abaqusexplicit is very general adaptive meshing is very costeffective in an explicit framework. As a result, the deformation process is split into a pure lagrangian phase and a pure eulerian phase combined with a smoothing phase. The impacting forces are transferred to the lagrangian structure through eulerianlagrangian contact which is based on the penalty contact algorithm. This paper presents the steps to achieve a fe model of the fsw process in the abaqusexplicit software, using the coupled eulerianlagrangian formulation cel, the johnsoncook constitutive. An important concept is that the equations of motion of classical mechanics can be based on a variational principle. The paperboard however is modeled using the lagrangian description according to common practice at tetra pak. Compared to the classic lagrangian modeling of the bird, the analysis has proven to be more stable, and the results, such as and damage areas, physically more realistic.
The main task of the thesis is to evaluate if the recently implemented coupled eulerianlagrangian formulation in abaqus is a proper strategy of modelling the the sealing process. Arbitrary lagrangianeulerian finite element formulations. Large displacements assumed in the analysis usually cause convergence problems. Example 1 in figure 1 we show a box of mass m sliding down a ramp of mass m. Lagrangian dynamics most of the material presented in this chapter is taken from thornton and marion, chap. Abaqus explicit arbitrary lagrangian eulerian formulation ale orthogonal cutting of aisi 1045 extended check out more machining tutorials. Application of coupled eulerian lagrangian approach in metal forming simulations numerical simulations of materials forming processes require both powerful computers and advanced software. Visit the simulia resource center for more customer examples. The purpose of this technique is to avoid mesh problems when performing simulations that involve highextreme deformations. Escall on lecture 11 17 december, 20 institute of structural engineering method of finite elements ii 1. A lagrangian integration point finite element method for. Mar 03, 2017 this video is on cel modelling example in abaquscae 6.
This video shows you how to develop cel simulation model with example enables you to practice and reproduce the. Bird strike damage analysis in aircraft structures using abaqusexplicit and coupled eulerian lagrangian approach. Eulerianbased finite element formulations or attached to material e. Abaqus uses the updated lagrangian formulation stress measure abaqus always calculates cauchy true. I dont really know the procedure used in abaqus, but several fe codes prefer a tl approach for.
Introduction to lagrangian and hamiltonian mechanics. Hi everybody, i need to run a blast simulation in abaqus using cel technique. The arbitrary lagrangian eulerian ale method is an explicit numerical formulation which has become a standard tool to solve large deformation problems in solid mechanics. The new coupling of the eulerian domain and lagrangian domain makes new types of analysis capabilities available that may not have been available before, one of them being sloshing in a flexible tank. Alebased finite element simulations can alleviate many of the. There are two main ways of approaching problems that involve the motion of deformable materials the lagrangian way and the eulerian way. Polymer flow in package sealing process a coupled eulerian. An important concept is that the equations of motion of classical mechanics can be. An introduction to lagrangian and hamiltonian mechanics. Airplane structures, composites, bird strike, impact damage, coupled eulerian lagrangian analysis, contact, high lift devices, abaqus explicit. How to model eulerian regions in a coupled eulerianlagrangian simulation in abaqus.
The lagrangian f orm ulation of mec hanics reading assignmen t. Updated lagrangian formulation for incremental general nonlinear analysis. The finite element method for the analysis of nonlinear and. Before cel, tank sloshing in abaqus involved modeling the fluid as a deformable mesh within classical lagrangian framework 1. Hyperelastic material analysis using abaqus element,typec3d8rh,elsetone. It gives no new information theres no advantage to it. The impacting forces are transferred to the lagrangian structure through eulerian lagrangian contact which is based on the penalty contact algorithm. The book begins by applying lagranges equations to a number of mechanical systems. Regional contact information is listed in the front of each abaqus manual. However, its first application to metal cutting was reported by usui et al. The ramp moves without friction on the horizontal plane and is located by coordinate x1. However, its first application to metal cutting was.
Total lagrangian formulation where 0 e ij is the linear incremental strain, 0. Bird strike damage analysis in aircraft structures using. Konkol and balachowski, 2016 used abaqus to compare lagrangian and ale. The coupled eulerianlagrangian cel approach in abaqus which provides engineers and scientists with the ability to simulate a class of problems where the interaction between structures and fluids is. How to model eulerian regions in a coupled eulerian lagrangian simulation in abaqus. By contrast, in an eulerian analysis nodes are fixed in space, and material flows through elements that do not deform.
The tutorial is intended to serve as a quick introduction to the software for the students in professor des mane 4240civl 4240 course at rpi and should, in no way, be deemed as a replacement of the official documentation distributed by the company that sells this software. Abaqus high level of detail manual design of workpiece and tool, free model. Both methods give exactly the same equations kr mgcos. Ivancevic department of aeronautical engineering, faculty of mechanical engineering and naval. This paper introduces the coupled eulerianlagrangian cel formulation, in which the. Learn how to setup a coupled eulerianlagrangian cel model of the moulding process of a polymeric bottle. Examples in lagrangian mechanics bloomington, indiana. Free abaqus tutorials to build and expand your experience on simulia abaqus fea software. For some reason, i am writing a finite element program using the timoshenko beam element and total lagrangian formulation for geometric nonlinear analysis.
Coupled euler lagrangian approach using abaqus explicit in. Theory, implementation, and practice november 9, 2010 springer. This type of adaptive meshing is often referred to as arbitrary lagrangianeulerian ale analysis. Some topics can be found in the abaqus manual 14 and others are experience. Although the adaptive meshing techniques and the user interface are similar in abaqus explicit and abaqus standard, the usecases and the level of functionality are different. Its original prescription rested on two principles. Total lagrangian explicit dynamics finite element algorithm for. The main improvement has been achieved by replacing the lagrange bird model with the coupled eulerian lagrangian formulation implemented in abaqus. The adaptive meshing technique in abaqus combines the features of pure lagrangian analysis and pure eulerian analysis. A students guide to lagrangians and hamiltonians a concise but rigorous treatment of variational techniques, focusing primarily on lagrangian and hamiltonian systems, this book is ideal for physics, engineering and mathematics students. I will assign similar problems for the next problem set. Lagrangian formulation, which is based on the concept of material coordinates lagrangian coordinates. The approach taken is mathematical in nature with a strong focus on the.
The main task of the thesis is to evaluate if the recently implemented coupled eulerian lagrangian formulation in abaqus is a proper strategy of modelling the the sealing process. It does not attempt to minimize discretization errors in smalldeformation analyses. Abaqus coupled eulerian lagrangian cel modelling tutorial. The interaction behaviour between the two is modelled by contact definition. Abaqus explicit arbitrary lagrangian eulerian formulation. Nonlinear elastic analysis using abaqus 24 2d solid continuum elements plane strain. This additivity states that the equations of motion of part a can not be dependent on. Paper open access related content numerical simulation. Chapter 3, elements, describes the element formulations. The arbitrary lagrangian eulerian ale method is an explicit numerical for mulation which has become a standard tool to solve large deformation problems in solid mechanics. Interaction between structure and water in seismic analyses of nuclear facilities cecilia rydell1, tobias gasch 2, luca facciolo3, daniel eriksson and richard malm4. This video is on cel modelling example in abaquscae 6. The lagrangian point of view is used for the mechanical modeling capabilities in abaqus. Readers are referred to abaqus analysis users manual 22.
Coupled eulerianlagrangian abaqus dassault systemes. Contrary to the lagrangian formulation, is the eulerian formulation where the mesh is spatially fixed. In our ellipsis code, the problem domain is represented by an eulerian mesh and an embedded set of lagrangian integration points or particles. In abaqus program the coupled eulerianlagrangian analysis is restricted. Eulerian analysis massachusetts institute of technology.
Eulerian elements may not always be 100% full of materialmany may be partially or completely void. Coupled eulerian lagrange cel analysis with abaqus. Application of an uncoupled aleformulation to confined. When does abaqus use the total lagrangian and when the updated lagrangian formulation. Total and updated lagrangian formulations imechanica.
When does abaqus use the total lagrangian and when the. Hi astlaia2002, it is stated that the elements are formulated in the current configuration using current nodal positions when nlgeom option is specified abaqus standard manual analysis analysis types introduction therefore, the updated lagrangian formulation is used when nlgeom is specified. Paper open access related content numerical simulation of the. Apr 12, 2016 abaqus explicit arbitrary lagrangian eulerian formulation ale orthogonal cutting of aisi 1045 extended check out more machining tutorials. Arbitrary lagrangian eulerian finite element formulations applied to geotechnical problems montaser bakroon, reza daryaei, daniel aubram, frank rackwitz abstract. Lagrangian extended finite element formulation for simulating large. The tutorial is intended to serve as a quick introduction to the software for the students in professor des mane 4240civl 4240 course at rpi and. Improving mesh quality increases the stable time increment size, which makes up for the added cost of the adaptive mesh increments.
Mechanics is that lagrangian mechanics is introduced in its. Coupled eulerian lagrange cel analysis with abaqus this analysis techniques combines two mesh approacheslagrangian and eulerianin the same analysis. A benchmark example of a simple tank sloshing problem is included to evaluate the use of different fsi methods. For uel, i think the user may choose either formulating in updated or total lagrangian. Application of coupled eulerianlagrangian approach in metal forming simulations numerical simulations of materials forming processes require both powerful computers and advanced software. In a pure lagrangian formulation each individual node of the computational mesh is permanently connected to the same material point during motion. The uncoupled approach has some advantages with respect. In this handout, we will discuss a lagrangian finite element formulation for large deformations. Lagranges equations are also used in optimization problems of dynamic systems. Consequently, lagrangian mechanics becomes the centerpiece of the course and provides a continous thread throughout the text.
Arbitrary lagrangianeulerian finite element formulations applied to geotechnical problems montaser bakroon, reza daryaei, daniel aubram, frank rackwitz abstract. Lagrangian mechanics our introduction to quantum mechanics will be based on its correspondence to classical mechanics. Adaptive meshing is supported for all stepdependent features. I am suspecting the problem may be caused by the use of nonvector rotational variables.
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