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The Largest Independant Solid Edge Resource Outside UGS
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SeGuruCool The Largest Independant Solid Edge Resource Outside UGS |
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www.oocities.org/SeGuruCool  segurucool @ indiatimes.com |
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Types of Analysis FEA, or finite element analysis, is a technique for predicting the response of structures and materials to environmental factors such as forces, heat and vibration. The process starts with the creation of a geometric model. Then, the model is subdivided (meshed) into small pieces (elements) of simple shapes connected at specific node points. In this manner, the stress-strain relationships are more easily approximated. Finally, the material behavior and the boundary conditions are applied to each element |  |
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Linear Static Analysis When loads are applied to a body, the body deforms and the effect of loads is transmitted throughout the body. The external loads induce internal forces and reactions to render the body into a state of equilibrium. Linear Static analysis calculates displacements, strains, stresses, and reaction forces under the effect of applied loads. |  |
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Assumptions in Linear Static Analysis Linear static analysis makes the following assumptions Static Assumption All loads are applied slowly and gradually until they reach their full magnitudes. After reaching their full magnitudes, loads remain constant (time-invariant). This assumption allows us to neglect inertial and damping forces due to negligibly small accelerations and velocities. |  |
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Linearity Assumption The relationship between loads and induced responses is linear. For example, if you double the loads, the response of the model (displacements, strains, and stresses), will also double. You can make the linearity assumption if: |  |
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Frequency Analysis Every structure has the tendency to vibrate at certain frequencies, called natural or resonant frequencies. Each natural frequency is associated with a certain shape, called mode shape, that the model tends to assume when vibrating at that frequency. When a structure is properly excited by dynamic loads that coincide with one of its natural frequencies, the structure undergoes large displacements. This phenomena is known as resonance. |  |
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For undamped systems, resonance theoretically causes infinite motion. Damping, however, always exists and it puts a limit on the response of the structures due to resonant loads. A continuous model has an infinite number of natural frequencies. However, a finite element model has a finite number of natural frequencies that is equal to the number of degrees of freedom considered in the model. The natural frequencies and corresponding mode shapes depend on the geometry of the structure, its material properties, and its support conditions. The computation of natural frequencies and mode shapes is known as modal, frequency, or normal mode analysis. |  |
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Buckling Analysis Models with thin parts tend to buckle under axial loading. Buckling can be defined as the sudden deformation which occurs when the stored membrane (axial) energy is converted into bending energy with no change in the externally applied loads. Mathematically, when buckling occurs, the total stiffness matrix becomes singular. The Linearized Buckling approach solves an eignvalue problem to estimate the critical buckling factors and the associated buckling shapes. Buckling analysis calculates the smallest (critical) loading required to buckle a model. Buckling loads are associated with buckling modes. Designers are usually interested in the lowest mode because it is associated with the lowest critical load. When buckling is the critical design factor, calculating multiple buckling modes helps in locating the weak areas of the model. This may prevent the occurrence of lower buckling modes by simple modifications. |  |
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Thermal Analysis Thermal analysis calculates the temperature distribution in a body due to some or all of the three mechanisms of heat transfer. viz : In all three mechanisms, heat energy flows from the medium with higher temperature to the medium with lower temperature. Heat transfer by conduction and convection requires the presence of an intervening medium while heat transfer by radiation does not. |  |
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Thermal Analysis - Conduction Conduction is the heat transfer mechanism in which thermal energy transfers from one point to another through the interaction between the atoms or molecules of the matter. Conduction occurs in solids, liquids, and gasses. For example, a hot cup of coffee on your desk eventually cools down to the room temperature partly due to conduction from the coffee directly to the air and through the body of the cup. Conduction does not involve any bulk motion of matter. The rate of heat conduction through a plane layer of thickness X is proportional to the heat transfer area and the temperature gradient, and inversely proportional to the thickness of the layer. Qcond = K A (T1 - T2) / X = K A dT/dx where K, called the thermal conductivity, measures the ability of a material to conduct heat and dT/dx is the temperature gradient. The units of K are W/m.oC or (Btu/s)/in.oF |  |
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Thermal Analysis - Convection Convection is the heat transfer mode in which heat transfers between a solid face and an adjacent moving fluid (or gas). Convection involves the combined effects of conduction and the moving fluid. The fluid particles act as carriers of thermal energy. The rate of heat exchange between the fluid of temperature Tf and a face of a solid of area A and temperature Ts can be expressed as: Qconvection = h A (Ts - Tf) where h is the convection heat transfer coefficient, Tf is the temperature of the fluid away from the face of the solid. The units of h are W/m2.oC or Btu/s.in2.oF. Free (Natural) Convection. The motion of the fluid adjacent to a solid face is caused by the buoyancy forces induced by changes in the density of the fluid due to the presence of the solid. When a hot plate is left to cool down in the air the particles of air adjacent to the face of the plate get warmer, their density decreases and hence they move upward. Forced Convection. An external means such as a fan or a pump is used to accelerate the flow of the fluid over the face of the solid. The rapid motion of the fluid particles over the face of the solid maximizes the temperature gradient and results in increasing the rate of heat exchange. |   |
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Thermal Analysis - Radiation Thermal radiation is the thermal energy emitted by bodies in the form of electromagnetic waves because of their temperature. All bodies with temperatures above the absolute zero emit thermal energy. Because electromagnetic waves travel in vacuum, no medium is necessary for radiation to take place. The thermal energy of the sun reaches earth by radiation. Because electromagnetic waves travel at the speed of light, radiation is the fastest heat transfer mechanism. Stefan-Boltzmann’s law Stefan-Boltzmann’s law states that the maximum rate of radiation that can be emitted by a surface of area A at a temperature Ts with a surrounding temperature Te is equal to : Qradiation = s A (T4s - T4e) where s is the Stefan-Boltzmann constant ( 5.67 x 10-8 W/m2.C4 or 3.3063 x 10-15 Btu/s.in2.F4 ). A surface that is emitting heat energy at this rate is called a black body. The ratio of the power per unit area radiated by a surface to that radiated by a black body at the same temperature is called emissivity (e). A black body therefore has an emissivity of 1 and a perfect reflector has an emissivity of 0. The view factor (f) is a measure for the exposure of the face to the ambient conditions. The value of view factor ranges from 1 (full exposure) to 0 (no exposure). Q = e Qmax = e f s A (T4s - T4a) where f is the view factor and e is the emissivity. You must define the emissivity (e), the ambient temperature, and the view factor to define radiation. |   |
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Design Optimization Optimization studies help you automate the search for the optimum solution. In optimizing a design, you need to define your objective (objective function), the dimensions of the design that can change (design variables), and the conditions that the design must satisfy (behavior constraints). For example, you may want to vary some of the dimensions in your model to minimize the material, while maintaining a safe level of stresses. In this case, your objective is to reduce the volume of the material, the varying dimensions are the design variables, and the condition that the stress level cannot exceed a certain limit is the behavior constraint. |
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Meshing FEA starts with the creation of a geometric model. Then, the program subdivides the model into small pieces of simple shapes (elements) connected at common points (nodes). Finite element analysis programs look at the model as a network of discrete interconnected elements. Linear elements are also called first-order, or lower-order elements. Parabolic elements are also called second-order, or higher-order elements. A linear tetrahedral element is defined by four corner nodes connected by six straight edges. A parabolic tetrahedral element is defined by four corner nodes, six mid-side nodes, and six edges. The figures show schematic drawings of linear and parabolic tetrahedral solid elements. |   |
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For the same mesh density (number of elements), parabolic elements yield better results than linear elements because:
1) they represent curved boundaries more accurately, and 2) they produce better mathematical approximations. However, parabolic elements require greater computational resources than linear elements. Each node in a solid element has three degrees of freedom which are the translations in three orthogonal directions. Normally the X, Y, and Z directions of the global Cartesian coordinate system are used in formulating the problem. For thermal problems, each node has one degree of freedom which is the temperaure. |  |
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Shell Meshing A linear triangular shell element is defined by three corner nodes connected by three straight edges. A parabolic triangular element is defined by three corner nodes, three mid-side nodes, and three parabolic edges. For studies created with the Shell mesh using mid-surface option, the thickness of the elements is automatically extracted from the geometry of the model. Shell elements are 2D elements capable of resisting membrane and bending loads. |   |
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For structural studies, each node in shell elements has six degrees of freedom; three translations and three rotations.
The translational degrees of freedom are motions in the global X, Y, and Z directions. The rotational degrees of freedom are rotations about the global X, Y, and Z axes. For thermal problems, each node has one degree of freedom which is the temperature. |  |
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Shell mesh using mid-surfaces This technique is used for sheet metals and simple thin solid parts with one material. The thickness of elements is calculated automatically based on surface pairs. This technique is not used for assemblies and surface models and can fail to generate the proper mesh for complex parts and parts with intersections. When using midplane meshing, view the mesh and see if it represents the actual model before proceeding with the solution. |  |
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Shell mesh using surfaces This option gives you full control on what faces or surfaces to mesh and what thickness and material to use for each face or surface. It is available for solid parts, assemblies, and surface models. Shell elements are placed such that the associated face or surface is located at the middle of the element across the thickness. |  |
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Mesh Quality (aspect ratio) Checks For a solid mesh, numerical accuracy is best achieved by a mesh with uniform perfect tetrahedral elements whose edges are equal in length. For a general geometry, it is not possible to create a mesh of perfect tetrahedral elements. Due to small edges, curved geometry, thin features, and sharp corners, some of the generated elements can have some of their edges much longer than others. When the edges of an element become much different in length, the accuracy of the results deteriorates. |   |
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Material Models A material model describes the stress-strain relation for a material. A linear elastic material model describes the elastic behavior of a material in the linear range. There are two types of material models: Linearity Assumptions The induced response is directly proportional to the applied loads. For example, if you double the magnitude of loads, the model's response (displacements, strains, and stresses) will double. You can make the linearity assumption if the following conditions are satisfied: Elasticity Assumption In other words, the model is assumed to be perfectly elastic. |  |
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Isotropic and Orthotropic Materials A material is isotropic if its mechanical and thermal properties are the same in all directions. Isotropic materials can have a homogeneous or non-homogeneous microscopic structures. For example, steel demonstrates isotropic behavior although its microscopic structure is non-homogeneous. A material is orthotropic if its mechanical or thermal properties are unique and independent in three mutually perpendicular directions. Examples of orthotropic materials are wood, many crystals, and rolled metals. For example, the mechanical properties of wood at a point are described in the longitudinal, radial, and tangential directions. The longitudinal axis is parallel to the grain (fiber) direction; the radial axis is normal to the growth rings; and the tangential axis is tangent to the growth rings. Orthotropic directions are defined with respect to a reference plane, axis, or coordinate system. For example, if you select an axis as a reference, X defines the radial direction, Y defines the tangential direction, and Z defines the axial direction. |   |
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Tushar Suradkar segurucool @ yahoo.com |
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