Analysis on the principle of finite elements (FEM/FEA)

Analysis on the principle of finite elements (FEM/FEA)
Óbuda University John von Neumann Faculty of Informatics Institute of Applied Mathematics Master in Mechatronics Course CAD Systems Laboratory No. 7 Analysis on the principle of finite elements (FEM/FEA) Dr. László Horváth

László Horváth UÓ-JNFI-IAM http://users.nik.uni-obuda.hu/lhorvath/
This presentation is intellectual property. It is available only for students in my courses. The screen shots in tis presentation was made in the CATIA V5 and V6 PLM systems the Laboratory of Intelligent Engineering systems, in real modeling process. The CATIA V5 és V6 PLM systems operate in the above laboratory by the help of Dassult Systémes Inc. and CAD-Terv Ltd. László Horváth UÓ-JNFI-IAM

Contents Engineering object as system Behavior of engineering objects Realistic simulation Finite element analysis Laboratory task 5.1 Definition, generating, and analysis of three dimensional shell mesh 5.2 Definition and generation of finite analysis model for solid body. Understanding results of analysis. László Horváth UÓ-JNFI-IAM

Engineering object as system
Call the technically meaningful object in object model simply as engineering object. Thus, an engineering object may be a surface, a self-contained unit or a product consisting of numerous units. Recently, requirements against results of engineering work need cooperation of several disciplines. The conventional mechanical functionality increasingly completed and replaced by embedded systems. Example: Drivers of vehicles and pilots of aircrafts operated drive chain through mechanical connection. In current products this is done through electronic systems. Paradigm shift was required from connected components to systems. Systems engineering methods are applied for the integration of disciplines. This require behavior modeling and simulation in multidisciplinary systems. László Horváth UÓ-JNFI-IAM

Engineering object as system
Engineering object is any object what needs definition and analysis in the course of any PLM activity. Higher level complex engineering object is considered as system. This object is a product, an unit of product, or an experimental configuration. Product consists of cooperating systems. By now, engineering work with systems inevitable. Engineering model is extended to the representation of systems by its organization in RFLP structure. Modeling of behaviors is done in the F and L levels of RFLP structure. This makes cooperation of various disciplines and global simulation of the related systems and subsystems possible. László Horváth UÓ-JNFI-IAM

Behavior of engineering objects
Behavior answers the question that how system handles relation of input and output and what is reaction of system for outside events. Requirement Requirements against product State logical behavior Function Functions to fulfill requirements Logical Structure of logical components. Dynamic behavior. Context dynamic behavior. Physical Physical level representations László Horváth UÓ-JNFI-IAM

Realistic simulation Important part of product development or experimental program in virtual space using model is finding that how will the elaborated object react to the effects from the real physical world. Multi physical problem is to be solved for multi-physics analysis of the response. This complex problem may involve linear and nonlinear solids, fluids, heat transfer, vibration, electromagnetic, and other elements. Coupled behavior is also to be modeled between multiply physical responses. Realistic simulation is a novel approach. It is aimed to assure realistic behavior representation of engineering objects. This behavior can be experienced during the operation of engineering object. Its analysis needs simulation of realistic operation environment. Behind most of simulations there is analysis based on principle of finite elements. László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements - general
It reveals effect of design variables on parameters which acting on engineering object performance Place dependent parameters are calculated. Analysis is done on finite number of finite elements. The method is approximation by finite elements in mash. Thus volume or surface is discretized. Parameters are calculated for nodes. Finite element method is a numerical method. Values of parameters are calculated using mathematical functions. Finite Element Modeling (FEM) and Finite Element Analysis (FEA) The method is suitable for calculation of parameters at any point of a solid when appropriate dimensioned elements are applied in accordance with requirements against analysis task. László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – short story
Analysis of the structural components in aircrafts involved new tasks which could not be feasible by traditional testing methods. Term was first time applied by Clough in 1960. First book: Zienkiwiecz és Chung, 1967. End of 60s: first solution for nonlinear problems. Oden, 1972: book about nonlinear problems. 70s: laying foundations in mathematics. By now, engineering virtual systems include or integrate this functionality. László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – FEM
Completed and simplified shape model Completing is done using reference elements (plane, line, midsurface, etc.) Simplification of intricate shapes with low load must provide equivalent model. Mesh of finite elements Node Edge Analyze, correct, improve and optimize mesh Load model: definition of loads and restraints and placing them in nodes in mesh or geometric elements in boundary. László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – finite elements
Type One dimensional Two dimensional shell Three dimensional shell Solid Degree of edge Linear- where shape is linear or linearization is allowable. One or two intermediate node can be defined to represent edge of two or three degrees, respectively. Pi elements: accurate fitting to geometry. Order of edges can be restricted (E. g. Max. order is 5). László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – loads and their effects
can vary in place and time represented by mathematical equation (typical examples): forces and temperatures at nodes Concentrated or distributed force or pressure on edges and surfaces, acceleration: gravitation or along line, circle, temperature in environment, Heat sources acting at nodes or distributed, heat conduction and radiation on face or edge, Magnetic field. Effects of loads Analyzed parameters (examples): stress, deformation, their gradient, pressure, inside force, reaction force, torque, strain energy, natural frequency, temperature, its gradient, heat flow, Magnetic field. At composite materials: analyses by layer and layer tear. László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – definition of loads and restraints Mesh is contextual with geometric model representation. Definition of loads: On point, edge, curve, surface, and section. On nodes and elements By mathematical function. On surface which passes over predefined points. Definition of restraints: Degrees of freedom. Base mechanical types for 1R, 1T, 2T, etc. Virtual part: by definition of 3T, 3R, implicit. Node displacement. Complex definition using several loads and restraints. László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – mesh generation methods
Essential functions Parametric mesh generation associative with geometric model on curves, surfaces, solids, Solids including holes, and inside cavities. Recognition of reference geometry. Recognition of nodes for further build of mesh. Grouping elements. Manually controlled automatic mesh generation Definition of global and local mesh density. Automatic density transition. Automatic mesh generation on geometry. User mesh definition points using points, curves, and surfaces. Specification of mesh distortion. Automatic minimal mesh distortion. Topological based generation. Mesh for group of surfaces. Sectioning on the basis of topology. Inactivating form features. Adaptive mesh generation Minimizing the mesh caused analysis error by automatic modification of Mesh density, element order, and element shape on a formerly generated coarse mesh. Analysis of error: normal, element distortion. Dividing element. Replacing node. Repeated meshing. In case of shell mesh different number of elements on opposite sides. László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – type of analysis
Linear The analyzed parameter is proportional to the load in the analysis range.. Static: The analyzed parameter does not change in the function of time. Dynamic: The analyzed parameter changes in the function of time: natural frequency, vibration. Nonlinear: It is taken into consideration that the analyzed parameter change to load is non linear in certain conditions. László Horváth UÓ-JNFI-IAM

Eigen frequency analysis
The frequency at which a system is tend to vibrate without any drive and damping force. Iso-static Restraint Statically definite restraining part where all rigid-body motion is impossible. Non-structural Mass Contribution to mass by features which have negligible structural stiffness. Surface Mass Density is defined for supports. László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – type of analysis
Example for static and dynamic solutions on the same mechanical part László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements – active analysis
Shape optimization Dimensions are proposed suitable for the design objectives in case of specified design constraints. Design objectives and constraints constitute the conditions of shape optimization. Typical tasks include simple shapes with high load. Examples: v a b Conditions of shape optimization Dimensions to be optimized, allowed range of dimensions, design constraints (allowed values) and design objectives: minimal weight of part, utilization of maximum allowed value of loads. László Horváth UÓ-JNFI-IAM

CS 7.1 laboratory exercise
Definition, generating, and analysis of three dimensional shell mesh László Horváth UÓ-JNFI-IAM

László Horváth UÓ-JNFI-IAM

Definition and generation of finite analysis model for solid body. Understanding results of analysis László Horváth UÓ-JNFI-IAM

László Horváth UÓ-JNFI-IAM

Analysis on the principle of finite elements (FEM/FEA)

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Analysis on the principle of finite elements (FEM/FEA)

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