preliminary decisions module 5 training manual january 30, 2001 inventory #001441 5-2 preliminary...
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Preliminary Decisions
Module 5
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Preliminary Decisions
Overview
• Before starting an analysis in ANSYS, you need to make a few decisions, such as the analysis type needed and the type of model you want to build.
• In this chapter, we will discuss some of the decision making process. The purpose is to give you an idea of the amount of planning generally needed before “jumping in” to do the analysis.
• Topics covered:
– A. Which analysis type?
– B. What to model?
– C. Which element type?
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Preliminary Decisions
A. Which analysis type?
• The analysis type usually belongs to one of the following disciplines:
Structural Motion of solid bodies, pressure on solid bodies, or contact of solid bodies
Thermal Applied heat, high temperatures, or changes in temperature
Electromagnetic Devices subjected to electric currents (AC or DC), electromagnetic waves, and voltage or charge excitation
Fluid Motion of gases/fluids, or contained gases/fluids
Coupled-Field Combinations of any of the above
• We will focus on structural analyses in this discussion.
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Preliminary Decisions
...Which analysis type?
• Once you choose a structural analysis, the next questions are:
– Static or dynamic analysis?
– Linear or nonlinear analysis?
• To answer these, remember that whenever a body is subjected to some excitation (loading), it responds with three types of forces:
– static forces (due to stiffness)
– inertia forces (due to mass)
– damping forces
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Preliminary Decisions
...Which analysis type?
Static vs. Dynamic Analysis
• A static analysis assumes that only the stiffness forces are significant.
• A dynamic analysis takes into account all three types of forces.
• For example, consider the analysis of a diving board.
– If the diver is standing still, it might be sufficient to do a static analysis.
– But if the diver is jumping up and down, you will need to do a dynamic analysis.
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...Which analysis type?
• Inertia and damping forces are usually significant if the applied loads vary rapidly with time.
• Therefore you can use time-dependency of loads as a way to choose between static and dynamic analysis.
– If the loading is constant over a relatively long period of time, choose a static analysis.
– Otherwise, choose a dynamic analysis.
• In general, if the excitation frequency is less than 1/3 of the structure’s lowest natural frequency, a static analysis may be acceptable.
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Preliminary Decisions
...Which analysis type?
Linear vs. Nonlinear Analysis
• A linear analysis assumes that the loading causes negligible changes to the stiffness of the structure. Typical characteristics are:
– Small deflections
– Strains and stresses within the elastic limit
– No abrupt changes in stiffness such as two bodies coming into and out of contact
Strain
Stress
Elastic modulus(EX)
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...Which analysis type?
• A nonlinear analysis is needed if the loading causes significant changes in the structure’s stiffness. Typical reasons for stiffness to change significantly are:
– Strains beyond the elastic limit (plasticity)
– Large deflections, such as with a loaded fishing rod
– Contact between two bodies
Strain
Stress
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Preliminary Decisions
B. What to Model?
• Many modeling decisions must be made before building an analysis model:
– How much detail should be included?
– Does symmetry apply?
– Will the model contain stress singularities?
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Preliminary Decisions
...What to Model?
Details
• Small details that are unimportant to the analysis should not be included in the analysis model. You can suppress such features before sending a model to ANSYS from a CAD system.
• For some structures, however, "small" details such as fillets or holes can be locations of maximum stress and might be quite important, depending on your analysis objectives.
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Preliminary Decisions
...What to Model?
Symmetry
• Many structures are symmetric in some form and allow only a representative portion or cross-section to be modeled.
• The main advantages of using a symmetric model are:
– It is generally easier to create the model.
– It allows you to make a finer, more detailed model and thereby obtain better results than would have been possible with the full model.
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...What to Model?
• To take advantage of symmetry, all of the following must be symmetric:
– Geometry
– Material properties
– Loading conditions
• There are different types of symmetry:
– Axisymmetry
– Rotational
– Planar or reflective
– Repetitive or translational
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Preliminary Decisions
...What to Model?
Axisymmetry
• Symmetry about a central axis, such as in light bulbs, straight pipes, cones, circular plates, and domes.
• Plane of symmetry is the cross-section anywhere around the structure. Thus you are using a single 2-D “slice” to represent 360° — a real savings in model size!
• Loading is also assumed to be axisymmetric in most cases. However, if it is not, and if the analysis is linear, the loads can be separated into harmonic components for independent solutions that can be superimposed.
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...What to Model?
Rotational symmetry
• Repeated segments arranged about a central axis, such as in turbine rotors.
• Only one segment of the structure needs to be modeled.
• Loading is also assumed to be symmetric about the axis.
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This model illustrates both reflective and
rotational symmetry
Preliminary Decisions
...What to Model?
Planar or reflective symmetry
• One half of the structure is a mirror image of the other half. The mirror is the plane of symmetry.
• Loading may be symmetric or anti-symmetric about the plane of symmetry.
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This model illustrates both repetitive and reflective symmetry.
Preliminary Decisions
...What to Model?
Repetitive or translational symmetry
• Repeated segments arranged along a straight line, such as a long pipe with evenly spaced cooling fins.
• Loading is also assumed to be “repeated” along the length of the model.
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Preliminary Decisions
...What to Model?
• In some cases, only a few minor details will disrupt a structure's symmetry. You may be able to ignore such details (or treat them as being symmetric) in order to gain the benefits of using a smaller model. How much accuracy is lost as the result of such a compromise might be difficult to estimate.
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Preliminary Decisions
...What to Model?
Stress singularities
• A stress singularity is a location in a finite element model where the stress value is unbounded (infinite). Examples:
– A point load, such as an applied force or moment
– An isolated constraint point, where the reaction force behaves like a point load
– A sharp re-entrant corner (with zero fillet radius)
• As the mesh density is refined ata stress singularity, the stress valueincreases and never converges.
P = P/AAs A 0,
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Preliminary Decisions
...What to Model?
• Real structures do not contain stress singularities. They are a fiction created by the simplifying assumptions of the model.
• So how do you deal with stress singularities?
– If they are located far away from the region of interest, you can simply ignore them by deactivating the affected zone while reviewing results.
– If they are located in the region of interest, you will need to take corrective action, such as:
• adding a fillet at re-entrant corners and reruning the analysis.
• replacing a point force with an equivalent pressure load.
• “spreading out” displacement constraints over a set of nodes.
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Preliminary Decisions
C. Which Element Type?
• This is an important decision you usually need to make before beginning the analysis.
• Typical issues are:
– Which element category? Solid, shell, beam, etc.
– Element order. Linear or quadratic.
– Mesh density. Usually determined by the objectives of the analysis.
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...Which Element Type?
Element category
• ANSYS offers many different categories of elements. Some of the commonly used ones are:
– Line elements
– Shells
– 2-D solids
– 3-D solids
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Preliminary Decisions
...Which Element Type?
• Line elements:
– Beam elements are used to model bolts, tubular members, C-sections, angle irons, or any long, slender members where only membrane and bending stresses are needed.
– Spar elements are used to model springs, bolts, preloaded bolts, and truss members.
– Spring elements are used to model springs, bolts, or long slender parts, or to replace complex parts by an equivalent stiffness.
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...Which Element Type?
• Shell elements:
– Used to model thin panels or curved surfaces.
– The definition of “thin” depends on the application, but as a general guideline, the major dimensions of the shell structure (panel) should be at least 10 times its thickness.
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• 2-D Solid elements:
– Used to model a cross-section of solid objects.
– Must be modeled in the global Cartesian X-Y plane.
– All loads are in the X-Y plane, and the response (displacements) are also in the X-Y plane.
– Element behavior may be one of the following:
• plane stress
• plane strain
• axisymmetric
• axisymmetric harmonic
Preliminary Decisions
...Which Element Type?
Y
X Z
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...Which Element Type?
• Plane stress assumes zero stress in the Z direction.
– Valid for components in which the Z dimension is smaller than the X and Y dimensions.
– Z-strain is non-zero.
– Optional thickness (Z direction) allowed.
– Used for structures such as flat plates subjected to in-plane loading, or thin disks under pressure or centrifugal loading.
Y
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...Which Element Type?
• Plane strain assumes zero strain in the Z direction.
– Valid for components in which the Z dimension is much larger than the X and Y dimensions.
– Z-stress is non-zero.
– Used for long, constant cross-section structures such as structural beams. Y X
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...Which Element Type?
• Axisymmetry assumes that the 3-D model and its loading can be generated by revolving a 2-D section 360° about the Y axis.
– Axis of symmetry must coincide with the global Y axis.
– Negative X coordinates are not permitted.
– Y direction is axial, X direction is radial, and Z direction is circumferential (hoop) direction.
– Hoop displacement is zero; hoop strains and stresses are usually very significant.
– Used for pressure vessels, straight pipes, shafts, etc.
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...Which Element Type?
• Axisymmetric harmonic is a special case of axisymmetry where the loads can be non-axisymmetric.
– The non-axisymmetric loading is decomposed into Fourier series components, applied and solved separately, and then combined later. No approximation is introduced by this simplification!
– Used for non-axisymmetric loads such as torque on a shaft.
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...Which Element Type?
• 3-D Solid elements:
– Used for structures which, because of geometry, materials, loading, or detail of required results, cannot be modeled with simpler elements.
– Also used when the model geometry is transferred from a 3-D CAD system, and a large amount of time and effort is required to convert it to a 2-D or shell form.
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...Which Element Type?
Element Order
• Element order refers to the polynomial order of the element’s shape functions.
• What is a shape function?
– It is a mathematical function that gives the “shape” of the results within the element. Since FEA solves for DOF values only at nodes, we need the shape function to map the nodal DOF values to points within the element.
– The shape function represents assumed behavior for a given element.
– How well each assumed element shape function matches the true behavior directly affects the accuracy of the solution, as shown on the next slide.
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Quadratic distribution of DOF values
Actual quadratic curve
Linear approximation (Poor Results)
Preliminary Decisions
...Which Element Type?
Quadratic approximation (Best Results)
Linear approximation with multiple elements
(Better Results)
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Preliminary Decisions
...Which Element Type?
• When you choose an element type, you are implicitly choosing and accepting the element shape function assumed for that element type. Therefore, check the shape function information before you choose an element type.
• Typically, a linear element has only corner nodes, whereas a quadratic element also has midside nodes.
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Preliminary Decisions
...Which Element Type?
Linear elements
• Can support only a linear variation of displacement and therefore (mostly) only a constant state of stress within a single element.
• Highly sensitive to element distortion.
• Acceptable if you are only interested in nominal stress results.
• Need to use a large number of elements to resolve high stress gradients.
Quadratic elements
• Can support a quadratic variation of displacement and therefore a linear variation of stress within a single element.
• Can represent curved edges and surfaces more accurately than linear elements. Not as sensitive to element distortion.
• Recommended if you are interested in highly accurate stresses.
• Give better results than linear elements, in many cases with fewer number of elements and total DOF.
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Preliminary Decisions
...Which Element Type?
• Notes:
– For shell models, the difference between linear and quadratic elements is not as dramatic as for solid models. Linear shells are therefore usually preferred.
– Besides linear and quadratic elements, a third kind is available, known as p-elements. P-elements can support anywhere from a quadratic to an 8th-order variation of displacement within a single element and include automatic solution convergence controls.
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Preliminary Decisions
...Which Element Type?
Mesh Density
• The fundamental premise of FEA is that as the number of elements (mesh density) is increased, the solution gets closer and closer to the true solution.
• However, solution time and computer resources required also increase dramatically as you increase the number of elements.
• The objectives of the analysis usually decide which way the slider bar below should be moved.
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Preliminary Decisions
...Which Element Type?
• If you are interested in highly accurate stresses:
– A fine mesh will be needed, omitting no geometric details at any location in the structure where such accuracy is needed.
– Stress convergence should be demonstrated.
– Any simplification anywhere in the model might introduce significant error.
• If you are interested in deflections or nominal stresses:
– A relatively coarse mesh is sufficient.
– Small geometry details may be omitted.
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...Which Element Type?
• If you are interested in mode shapes (modal analysis):
– Small details can usually be omitted.
– Simple mode shapes can be captured using a relatively coarse mesh.
– Complex mode shapes may require a uniform, moderately fine mesh.
• Thermal Analyses:
– Small details can usually be omitted, but since many thermal analyses are followed by a stress analysis, stress considerations generally dictate the detail of the model.
– Mesh density is usually determined by expected thermal gradients. A fine mesh is required for high thermal gradients, whereas a coarse mesh may be sufficient for low gradients.
