Chapter Four Static Structural Analysis Linear Static Structural

Chapter Four Static Structural Analysis

Linear Static Structural Analysis Chapter Overview Training Manual – Geometry and Elements – Contact and Types of Supported Assemblies – Environment, including Loads and Supports – Solving Models – Results and Postprocessing • The capabilities described in this section are generally applicable to ANSYS Design. Space Entra licenses and above. – Some options discussed in this chapter may require more advanced licenses, but these are noted accordingly. ANSYS Workbench – Simulation • In this chapter, performing linear static structural analyses in Simulation will be covered: – Free vibration, harmonic, and nonlinear structural analyses are August 26, 2005 not discussed here but in their respective chapters. Inventory #002265 4 -2

Linear Static Structural Analysis Basics of Linear Static Analysis Training Manual Assumptions: – [K] is constant • Linear elastic material behavior is assumed • Small deflection theory is used • Some nonlinear boundary conditions may be included – {F} is statically applied • No time-varying forces are considered • No inertial effects (mass, damping) are included • It is important to remember these assumptions related to linear static analysis. Nonlinear static and dynamic analyses are covered in later chapters. ANSYS Workbench – Simulation • For a linear static structural analysis, the displacements {x} are solved for in the matrix equation below: August 26, 2005 Inventory #002265 4 -3

Linear Static Structural Analysis A. Geometry Training Manual • For surface bodies, thickness must be supplied in the “Details” view of the “Geometry” branch. • The cross-section and orientation of line bodies are defined within Design. Modeler and are imported into Simulation automatically. – For line bodies, only displacement results are available. ANSYS Workbench – Simulation • In structural analyses, all types of bodies supported by Simulation may be used. August 26, 2005 Inventory #002265 4 -4

Linear Static Structural Analysis … Point Mass Training Manual – A point mass is associated with surface(s) only – The location can be defined by either: • (x, y, z) coordinates in any user-defined Coordinate System • Selecting vertices/edges/surfaces to define location – In a structural static analysis, the point mass is affected by “Acceleration, ” “Standard Earth Gravity, ” and “Rotational Velocity”. No other loads affect a point mass. – The mass is ‘connected’ to selected surfaces assuming no stiffness between them. – No rotational inertial terms are present. ANSYS Workbench – Simulation • A Point Mass is available under the Geometry branch to mimic weight not explicitly modeled August 26, 2005 Inventory #002265 4 -5

Linear Static Structural Analysis … Point Mass Training Manual – a point mass in a linear static analysis can be used to account for the additional mass of a structure not modeled – No results are obtained for the Point Mass itself ANSYS Workbench – Simulation • A point mass will be displayed as a round, grey sphere August 26, 2005 Inventory #002265 4 -6

Linear Static Structural Analysis … Material Properties Training Manual – Material input is handled in the “Engineering Data” application – Materials are assigned per part in the geometry branch – Mass density is required if any inertial loads are present – Thermal expansion coefficient and thermal conductivity are required if any thermal loads are present – Stress Limits are needed if a Stress Tool result is present – Fatigue Properties are needed if Fatigue Tool result is present • Requires Fatigue Module add-on license ANSYS Workbench – Simulation • Young’s Modulus and Poisson’s Ratio are required for linear static structural analyses August 26, 2005 Inventory #002265 4 -7

Linear Static Structural Analysis … Material Properties ANSYS Workbench – Simulation • Engineering Data view shown below: Training Manual August 26, 2005 Inventory #002265 4 -8

Linear Static Structural Analysis B. Assemblies – Solid Body Contact Training Manual – Contact allows non-matching meshes at boundaries between solid parts – Tolerance controls under “Contact” branch allows the user to specify distance of auto contact detection via slider bar ANSYS Workbench – Simulation • When importing assemblies of solid parts, contact regions are automatically created between the solid bodies. August 26, 2005 Inventory #002265 4 -9

Linear Static Structural Analysis … Assemblies – Solid Body Contact Training Manual – One side of a contact region is referred to as a contact surface, the other side is referred to as a target surface – The contact surfaces are restricted from penetrating through the target surfaces however the opposite is not true • When one side is the contact and the other side is the target, this is called asymmetric contact. If both sides are made to be contact & target this is called symmetric contact • By default, Simulation uses symmetric contact for solid assemblies • For ANSYS Professional licenses and above, the user may change to asymmetric contact, as desired ANSYS Workbench – Simulation • In Simulation, the concept of contact and target surfaces are used for each contact region August 26, 2005 Inventory #002265 4 -10

Linear Static Structural Analysis … Assemblies – Solid Body Contact – Bonded and No Separation contact are basically linear and require only 1 iteration – Frictionless and Rough contact are nonlinear and require multiple iterations (small deflection theory is still assumed) • An “interface treatment” option is available: – “Add Offset”: input zero or non-zero value for initial adjustment – “Adjusted to Touch”: ANSYS closes any gap to a just touching position (ANSYS Professional and above) ANSYS Workbench – Simulation • Four contact types are available: Training Manual August 26, 2005 Inventory #002265 4 -11

Linear Static Structural Analysis … Assemblies – Solid Body Contact – Formulation can be changed from “Pure Penalty” to “Augmented Lagrange, ” “MPC, ” or “Normal Lagrange. ” • “MPC” is applicable to bonded contact only • “Augmented Lagrange” is used in classic ANSYS • Note: the MPC formulation writes constraint equations relating the movement of parts at an interface. This can be an attractive alternative to penalty method for bonded contact. • Additional information on advanced contact is presented in the Workbench nonlinear course as well as the ANSYS documentation ANSYS Workbench – Simulation • For the advanced user, some of the contact options can be modified Training Manual August 26, 2005 Inventory #002265 4 -12

Linear Static Structural Analysis … Assemblies – Solid Body Contact ANSYS Workbench – Simulation • Advanced options (continued): Training Manual – Pin Ball Region: • Inside pinball = near-field contact • Outside pinball = far-field contact • Allows the solver to more efficiently process contact calculations • Other advanced contact options will be discussed in Chapter 11. In this case, the gap between the two parts is bigger than the pinball region, so no automatic gap closure will be performed. August 26, 2005 Inventory #002265 4 -13

Linear Static Structural Analysis … Assemblies – Surface Body Contact – More contact options are exposed to the user – Contact postprocessing is also available (discussed later) ANSYS Workbench – Simulation • For ANSYS Professional licenses and above, mixed assemblies of shells and solids are supported Training Manual August 26, 2005 Inventory #002265 4 -14

Linear Static Structural Analysis … Assemblies – Surface Body Contact – For contact including shell faces or solid edges, only bonded or no separation behavior is allowed – For contact involving shell edges, only bonded behavior using MPC formulation is allowed • If a gap exists the pinball region can be used to detect contact beyond the gap. ANSYS Workbench – Simulation • Edge contact is a subset of general contact Training Manual August 26, 2005 Inventory #002265 4 -15

Linear Static Structural Analysis … Assemblies – Contact Summary ANSYS Workbench – Simulation • Summary of contact types and options available in Simulation: Training Manual August 26, 2005 Inventory #002265 4 -16

Linear Static Structural Analysis … Assemblies – Spot Weld Training Manual – Spotweld definition is done in the CAD software. Currently, only Design. Modeler and Unigraphics define spotwelds in a manner that Simulation supports. – Spotwelds can also be created in Simulation manually, but only at discrete vertices. ANSYS Workbench – Simulation • Spot welds provide a means of connecting shell assemblies at discrete points August 26, 2005 Inventory #002265 4 -17

Linear Static Structural Analysis C. Loads and Supports Training Manual – Inertial loads • These loads act on the entire system • Density is required for mass calculations • These are only loads which act on defined Point Masses – Structural Loads • These are forces or moments acting on parts of the system – Structural Supports • These are constraints that prevent movement on certain regions – Thermal Loads • Structurally speaking, thermal loads result in a temperature field, which causes thermal expansion on the model. ANSYS Workbench – Simulation • There are four types of structural loads available: August 26, 2005 Inventory #002265 4 -18

Linear Static Structural Analysis . . . Time Type Training Manual • The default time type for loading is “static” • “Transient” and “harmonic” time types are available as options • Sequence loading allows a series of static time steps to be set up in advance and solved at once • Sequenced results can be reviewed step by step ANSYS Workbench – Simulation • A time type option is available at certain license levels August 26, 2005 Inventory #002265 4 -19

Linear Static Structural Analysis . . . Time Type • Enter the value of the load for each step by first highlighting the desired step in the graphics window. • The chart in the graphics window displays the variation of the load while a legend in the graphics window displays the current view setting. ANSYS Workbench – Simulation • Specify the desired number of sequence steps in the “Steps” field in the main toolbar. Training Manual August 26, 2005 Inventory #002265 4 -20

Linear Static Structural Analysis . . . Time Type Results of a sequenced simulation can be reviewed by highlighting the solution of interest on the graph, “RMB > Retrieve Results”. ANSYS Workbench – Simulation • Training Manual August 26, 2005 Inventory #002265 4 -21

Linear Static Structural Analysis … Directional Loads Training Manual – In the Details view, change “Define By” to “Components”. Then, select the appropriate CS from the pull-down menu. – Specify x, y, and/or z components, which are relative to the selected Coordinate System – Not all loads/supports support use of CS: Loads/Supports not listed in the table do not have direction associated with it, so Coordinate Systems are not applicable. ANSYS Workbench – Simulation • For most loads/supports which have an orientation, the direction can be defined by components in any Coordinate System August 26, 2005 Inventory #002265 4 -22

Linear Static Structural Analysis … Acceleration & Gravity Training Manual – Acts on entire model in length/time 2 units. – Note, inertial forces are in the opposite direction to applied acceleration – Acceleration can be defined by Components or Vector • Standard Earth Gravity: – Value applied is 9. 80665 m/s 2 (in SI units) – Standard Earth Gravity direction can only be defined along one of three World Coordinate System axes – “Standard Earth Gravity” is defined as an acceleration. Define the direction opposite to gravitational force ANSYS Workbench – Simulation • Acceleration: August 26, 2005 Inventory #002265 4 -23

Linear Static Structural Analysis … Rotational Velocity Training Manual – Entire model spins about an axis at a given rate – Define by vector using geometry for axis of rotation – Define by components supplying origin and components in global or local coordinate system – Input can be in radians per second (default) or RPM ANSYS Workbench – Simulation • Rotational velocity: August 26, 2005 Inventory #002265 4 -24

Linear Static Structural Analysis … Forces and Pressures – Applied to surfaces, acts normal to the surface – Positive value into surface, negative value acts out of surface – Units of pressure are in force per area • Force loading: – Forces can be applied on vertices, edges, or surfaces. – The force will be evenly distributed on all entities. Units are mass*length/time 2 – Force can be defined via vector or component methods ANSYS Workbench – Simulation • Pressure loading: Training Manual August 26, 2005 Inventory #002265 4 -25

Linear Static Structural Analysis … Bearing Load – Radial component will be distributed on compressive side using projected area (see below) – Axial component is distributed evenly on cylinder – Use only one bearing load per cylindrical surface. If the cylindrical surface is split be sure to select both halves of cylindrical surface when applying this load. – Load is in units of force – Bearing load can be defined via vector or component method ANSYS Workbench – Simulation • Bearing Load (cylindrical surfaces only): Training Manual August 26, 2005 Inventory #002265 4 -26

Linear Static Structural Analysis … Moment Load Training Manual – For solid bodies, a moment can be applied on any surface – If multiple surfaces are selected, the moment load is evenly distributed – Vector or component method can be used. The moment acts about the vector using the right-hand rule – For surface bodies, a moment can also be applied to a vertex or edge with similar definition – Units of moment are in Force*length. ANSYS Workbench – Simulation • Moment Load: August 26, 2005 Inventory #002265 4 -27

Linear Static Structural Analysis … Remote Load Training Manual – applies an offset force on a surface or edge of a surface body – The user supplies the origin of the force (vertices, cylinder or x, y, z coordinates). A user-defined Coordinate System may be used to reference the location. – Can be defined using vector or component method – Applies an equivalent force and moment on the surface – Units are in force (mass*length/time 2) Load transfer surface ANSYS Workbench – Simulation • Remote Load: August 26, 2005 Inventory #002265 4 -28

Linear Static Structural Analysis . . . Bolt Load Training Manual – Applies a pretension load to a cylindrical section simulating bolt tightening – Apply pretension load (force) or adjustment (length) as initial condition – For sequenced loading additional options are available (see next page) ANSYS Workbench – Simulation • Bolt Load: August 26, 2005 Inventory #002265 4 -29

Linear Static Structural Analysis . . . Bolt Load For static analyses the preload is applied in an initial solution and external loads are applied in a subsequent solution – Note this 2 step sequence is automatic and transparent • The bolt load is automatically locked during the second solution • For sequence analyses users may choose to lock or open the bolt load in any load step except the first ANSYS Workbench – Simulation • Training Manual August 26, 2005 Inventory #002265 4 -30

Linear Static Structural Analysis . . . Bolt Load Training Manual – Can be used only in 3 D simulations – Can be applied to cylindrical surfaces or bodies. Bodies require a local coordinate system with the Z axis representing the pretension direction – A refined mesh is recommended (must be more than 1 element along the bolt section) ANSYS Workbench – Simulation • Bolt Load Tips: August 26, 2005 Inventory #002265 4 -31

Linear Static Structural Analysis … Supports (General) Training Manual – Constraints all degrees of freedom on vertex, edge, or surface • Solid bodies: constrains x, y, and z • Surface and line bodies: constrains x, y, z, rotx, roty and rotz • Given Displacement: – Applies known displacement on vertex, edge, or surface – Allows for imposed translational displacement in x, y, and z (in user-defined Coordinate System) – Entering “ 0” means that the direction is constrained. – Leaving the direction blank means that the entity is free to move in that direction ANSYS Workbench – Simulation • Fixed Support: August 26, 2005 Inventory #002265 4 -32

Linear Static Structural Analysis … Supports (Solid Bodies) Training Manual – Applies constraint in normal direction on surfaces – For solid bodies, this support can be used to apply a ‘symmetry’ plane boundary condition since ‘symmetry’ plane is same as normal constraint • Cylindrical Constraint: – Applied on cylindrical surfaces – User can specify whether axial, radial, or tangential components are constrained – Suitable for small-deflection (linear) analysis only ANSYS Workbench – Simulation • Frictionless Support: August 26, 2005 Inventory #002265 4 -33

Linear Static Structural Analysis … Supports (Solid Bodies) Training Manual – Applies a constraint in the normal compressive direction – Can be used on a cylindrical surface to model a pin (referred to as “Pinned Cylinder” 7. 1) – Notice in the example above the outline of the undeformed cylinder is shown. The compressive side retains the shape of the original cylinder, but the tensile side is free to deform. ANSYS Workbench – Simulation • Compression Only Support: – This requires an iterative (nonlinear) solution. August 26, 2005 Inventory #002265 4 -34

Linear Static Structural Analysis … Supports (Line/Surface Bodies) Training Manual – Can be applied on edge or vertex of surface or line bodies – Prevents all translations but all rotations are free • Fixed Rotation: – Can be applied on surface, edge, or vertex of surface or line bodies – Constrains rotations but translations are free ANSYS Workbench – Simulation • Simply Supported: August 26, 2005 Inventory #002265 4 -35

Linear Static Structural Analysis … Thermal Loading Training Manual – Thermal strains are calculated as follows: where a is thermal expansion coefficient (CTE), Tref is the reference temperature at which thermal strains are zero, T is the applied temperature, and eth is thermal strain. – CTE is a material property defined in “Engineering Data” and has units of strain per temperature – The reference temperature is defined in the “Environment” branch ANSYS Workbench – Simulation • Temperature causes thermal expansion in the model August 26, 2005 Inventory #002265 4 -36

Linear Static Structural Analysis … Thermal Loading Training Manual – Any temperature loading can be applied (see Chapter 6 on Thermal Analysis for details) – Simulation will always perform a thermal solution first, then use the calculated temperature field as input when solving the structural solution. ANSYS Workbench – Simulation • Thermal loads: August 26, 2005 Inventory #002265 4 -37

Linear Static Structural Analysis D. Workshop 4. 1 – Linear Structural Analysis • Goal: – A 5 part assembly representing an impeller type pump is analyzed with a 100 N preload on the belt. ANSYS Workbench – Simulation • Workshop 4. 1 – Linear Structural Analysis Training Manual August 26, 2005 Inventory #002265 4 -38

Linear Static Structural Analysis E. Solution Options – Save ANSYS db: • Useful if you want to open a database in ANSYS – Two solvers are available in Simulation: • The “Direct” solver is useful for models containing thin surface and line bodies. It is a robust solver and handles any situation (Sparse solver in ANSYS) • The “Iterative” solver is most efficient when solving large, bulky solid bodies. It can handle large models well, although it is less efficient for beam/shells (PCG solver in ANSYS) ANSYS Workbench – Simulation • Solution options can be set under the “Solution” branch Training Manual August 26, 2005 Inventory #002265 4 -39

Linear Static Structural Analysis … Solution Options Training Manual • If “Program Controlled” is set, Simulation tries to anticipate underconstrained models. If no “Fixed Support” is present, it may add weak springs and provide an informative message letting the user know that it has done so • This can be set to “On” or “Off”. ANSYS Workbench – Simulation – Weak springs can be added to stabilize model August 26, 2005 Inventory #002265 4 -40

Linear Static Structural Analysis … Solution Options • Analysis Type: Static Structural, thermal, etc • Nonlinear solution: indicated when options cause the solution to be nonlinear. These type of solutions require multiple iterations and take longer than linear solutions. • Solver Working Directory: – Location where scratch files are saved during solution – Default is the TEMP directory on Windows systems – Can be changed in “Tools > Options … > Simulation: Solution > Solver Working Directory” – Solver Messages: review messagges triggered during the solution by clicking “Solver Messages” field ANSYS Workbench – Simulation – Solution Information: Training Manual August 26, 2005 Inventory #002265 4 -41

Linear Static Structural Analysis … Solving the Model Training Manual – By default, two processors (if present) will be used for parallel processing. To set the number, use “Tools > Options … > Simulation: Solution > Number of Processors to Use” ANSYS Workbench – Simulation • To solve the model, request results first (covered next) and click on the “Solve” button on the Standard Toolbar August 26, 2005 Inventory #002265 4 -42

Linear Static Structural Analysis F. Results and Postprocessing Training Manual – Directional and total deformation – Components, principal, or invariants of stresses and strains – Contact output • Requires ANSYS Professional and above – Reaction forces • In Simulation, results are usually requested before solving, but they can be requested afterwards, too. – If you solve a model then request results afterwards, click on the “Solve” button , and the results will be retrieved. A new solution is not required for linear analyses ANSYS Workbench – Simulation • Various results are available for postprocessing: August 26, 2005 Inventory #002265 4 -43

Linear Static Structural Analysis … Plotting Results Training Manual ANSYS Workbench – Simulation • All of the contour and vector plots are usually shown on the deformed geometry. Use the Context Toolbar to change the scaling or display of results to desired settings. August 26, 2005 Inventory #002265 4 -44

Linear Static Structural Analysis … Deformation – Total deformation is a scalar quantity: – The x, y, and z components of deformation can be requested under “Directional. ” – if a “Coordinate System” branch is present, users can request directional results in a given coordinate system. – Vector plots of deformation are available. ANSYS Workbench – Simulation • The deformation of the model can be plotted: Training Manual August 26, 2005 Inventory #002265 4 -45

Linear Static Structural Analysis … Deformation Training Manual – Because deformation (displacements) are DOF which Simulation solves for, the convergence behavior is wellbehaved when using the Convergence tool ANSYS Workbench – Simulation • Deformation results are available for line, surface, and solid bodies August 26, 2005 Inventory #002265 4 -46

Linear Static Structural Analysis … Stresses and Strains Training Manual – Stresses and (elastic) strains have six components (x, y, z, xy, yz, xz) while thermal strains have three components (x, y, z) – For stresses and strains, components can be requested under “Normal” (x, y, z) and “Shear” (xy, yz, xz). For thermal strains, (x, y, z) components are under “Thermal. ” ANSYS Workbench – Simulation • Stresses and strains: August 26, 2005 Inventory #002265 4 -47

Linear Static Structural Analysis … Stress Tools – Ductile Theories: • Maximum Equivalent Stress • Maximum Shear Stress – Brittle Theories: • Mohr-Coulomb Stress • Maximum Tensile Stress – Within each stress tool safety factor, safety margin and stress ratio can be plotted ANSYS Workbench – Simulation • Safety Factors (choose from 4 failure theories): Training Manual August 26, 2005 Inventory #002265 4 -48

Linear Static Structural Analysis … Contact Results Training Manual • If asymmetric or auto-asymmetric contact is used, then contact results will be reported on the ‘contact’ surfaces only. The ‘target’ surfaces will report zero values, if requested. • If symmetric contact is used, then contact results will be reported on both surfaces. For values such as contact pressure, the actual contact pressure will be an average of both surfaces in contact. – Contact results are first requested via a “Contact Tool” under the Solution branch. ANSYS Workbench – Simulation • Contact Results: August 26, 2005 Inventory #002265 4 -49

Linear Static Structural Analysis … Contact Results Training Manual – The Worksheet view easily allows users to select which contact regions will be associated with the “Contact Tool” – Results on ‘contact’ or ‘target’ sides (or both) can be selected from the spreadsheet (symmetric vs. asymmetric contact) – Specific contact results chosen from Context Toolbar Select contact regions you want to review (add more “Contact Tool” branches to look at contact region output separately). Right-click on the worksheet to see other available options. For the “Contact Tool”, then request contact output results, and those results will correspond to selected contact regions. ANSYS Workbench – Simulation • The user can specify contact output under “Contact Tool” August 26, 2005 Inventory #002265 4 -50

Linear Static Structural Analysis … Contact Results Training Manual – Pressure: shows distribution of normal contact pressure – Penetration/Gap: shows the resulting amount of penetration or gap (within pinball radius). – Sliding Distance: distance one surface has slid with respect to the other. – Frictional Stress: is tangential contact traction due to frictional effects. – Status: open or closed • For the open state, near-field means that it is within pinball region, far-field means that it is outside of pinball region. Contour results are plotted with the rest of the model being translucent for easier viewing. ANSYS Workbench – Simulation • Contact Results: August 26, 2005 Inventory #002265 4 -51

Linear Static Structural Analysis … Contact Forces Contact Reactions: requested for “Contact Tool”, forces and moments are reported for the requested contact regions – Under the “Worksheet” tab, contact forces for all requested contact regions will be tabulated – Under the “Geometry” tab, symbols will show direction of contact forces and moments. ANSYS Workbench – Simulation • Training Manual August 26, 2005 Inventory #002265 4 -52

Linear Static Structural Analysis … Reaction Forces at Supports Training Manual – Reaction forces and moments are shown in the details for each support. X, Y, and Z components are reported with respect to the world coordinate system. Moments are reported at the centroid of the support. – The reaction force for weak springs, if used, are listed under the “Environment” branch Details. The weak spring reaction forces should be small to ensure that the effect of weak springs is negligible. ANSYS Workbench – Simulation • Reaction forces and moments are output for each support August 26, 2005 Inventory #002265 4 -53

Linear Static Structural Analysis … Reaction Forces at Supports Training Manual – If a support shares a vertex, edge, or surface with another support, contact pair, or load, the reported reaction forces may be incorrect. ANSYS Workbench – Simulation • The “Worksheet” tab for “Environment” branch has a summary of reaction forces and moments August 26, 2005 Inventory #002265 4 -54

Linear Static Structural Analysis … Fatigue Training Manual – The “Fatigue Tool” provides stress-based fatigue calculations to aid the design engineer with evaluating the life of components in the system – Constant or variable amplitude loading, proportional or nonproportional loading is possible Damage Matrix at Critical Location ANSYS Workbench – Simulation • If the Fatigue Module add-on license is available, additional post-processing involving fatigue calculations is possible Contour of Safety Factor August 26, 2005 Inventory #002265 4 -55

Linear Static Structural Analysis G. Workshop 4. 2 – 2 D vs 3 D Analysis Workshop 4. 2 – Comparing 2 D and 3 D Structural Analysis • Comparing 2 D and 3 D structural analyses. • Shown here are the 3 D sector model and the 2 D axisymmetric model. Pressure Cap Retaining Ring ANSYS Workbench – Simulation • Training Manual August 26, 2005 Inventory #002265 4 -56