ECIV 720 A Advanced Structural Mechanics and Analysis

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ECIV 720 A Advanced Structural Mechanics and
Analysis

• Solid Modeling

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Summary of Procedure
T
Nodes should be placed at
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Summary of Procedure
For Every Element Compute

• Strain-Displacement Matrix B

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Summary of Procedure

• Node Equivalent Body Force Vector

• Node Equivalent Traction Vector

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Summary of Procedure
Collect ALL Point Loads in Nodal Load Vector
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Summary of Procedure
Form Stiffness Equations
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Summary of Procedure
Apply Boundary Conditions
For Every Element Compute Stress
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Modeling Issues

• Data Preparation
• The three modes of typical FE software
• Pre-Processing
• Processing
• Post-Processing
• Solid Modeling
• Meshing
• Solution Convergence

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Data Processing
For a given physical problem select an
appropriate mathematical model e.g.
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Set Up General Model Data
Material Material Properties Properties Properties Properties
No Name E v r .
id Banana xxx xxx xxx xxx

Section Section Properties Properties Properties Properties
No Name A Ix Iy .
id Apple xxx xxx xxx xxx

Constants Constants Properties Properties Properties Properties
No Name P1 P2 P3 .
id Orange xxx xxx xxx xxx

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Set Up General Model Data
Element Groups Element Groups Options Properties Properties Properties
No Type Mat Sec Thk
1 1D Axial Tension id id n/a
2 1D Axial id id n/a
3 2D CST Plane stress id id id
4 2D CST Plane strain id id n/a
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Finite Element Mesh
May be Defined in
Direct Way
Solid Modeling approach

• Nodes
• Elements
• Loads
• BC

• Geometry of Solid
• Loads
• BC

Automatic Mesh Generation
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Direct FEM Mesh
Manually define nodes, elements, BC loads
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Direct FEM Mesh
Typical Input Data (Text File or GUI) Actual
depends on software
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Direct FEM Mesh
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Solid Modeling
Describe Geometry of FE Domain as a collection of
Primitive Entities
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Solid Modeling
Do not confuse with FEM node
Line
Any two points define a line
Points belong to line
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Solid Modeling
Surface
Any closed loop of lines define surface
Points belong to lines
Points AND lines belong to surface
2 faces are defined
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Solid Modeling
Volume
Any closed loop of faces defines volume
Points belong to lines
Points AND lines belong to surface
Points AND lines AND Surfaces belong to volume
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Solid Modeling
Primitive Entities can be used to form
more complex solid geometries
Boolean Operations
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Solid Modeling
Boolean Operations
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Solid Modeling
Each of the primitive or the derived entities
(objects) is assigned a set of properties such as
material, FEM type, etc.
Typically, derived objects inherit properties of
parents. At any point, such properties can be
changed
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Solid Modeling
Loads and Boundary Conditions can now be applied
on primitive objects regardless of the specific
Finite Elements.
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Automatic Meshing
Solid Model
Structured Mesh (Mapped)
Free Mesh
Triangulation Techniques
Based on Geometric Transformations
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Structured Mesh
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Structured Mesh
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Free Mesh
Triangulation Technique
Suitable for arbitrary geometries
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Example Using ANSYS
thickness1
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Plane Stress With Thickness E29x106
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5
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Define Element Groups
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Define Element Options
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Define Thickness
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Define Material
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Define Key points
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Defining Areas
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Deleting Entities
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Automatic Meshing - Coarse
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Applying Boundary Conditions
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Applying Loads
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Applying Loads
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Processing
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Deformed Shape
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Vertical Displacement
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sx
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sy
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Medium Mesh
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Vertical Displacement
Uy 0.002042 in
Compare to Uy 0.001905 in
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sx sy
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Refine Mesh
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Refined Mesh
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Displacement Uy
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sx sy
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Very Fine Mesh With Element Refinement
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Vertical Displacement
Uy 0.002084 in
Compare to Uy 0.002042 in Uy 0.001905 in
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Stress Concentration
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Stress Concentration
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sx
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sy
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COMMON MISTAKES
Data Input

• Material properties are zero in elements that
  share a node
• One or more structure nodes are not connected to
  an element
• One or more parts of the structure are not
  connected to the remainder
• Unspecified or inadequate boundary conditions

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COMMON MISTAKES
Data Input

• A spurious mode (mechanism) is possible because
  of inadequate connections
• Too many releases prescribed at a joint
• Large stiffness differences
• Part of the structure has buckled
• In nonlinear analysis, supports or connections
  have reached zero stiffness (part of structure
  inadequatly supported)

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COMMON MISTAKES
Results appear correct

• Elements are of the wrong type (shell elements
  used where solid elements required)
• Mesh is too coarse or element capability too
  limited
• Loads are wrong in location, type or direction
• Boundary conditions are wrong in location type or
  direction
• Decimal points misplaced or mixed units used

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COMMON MISTAKES
Results appear correct

• Element may be defined twice