ECIV 720 A Advanced Structural Mechanics and Analysis Solid Modeling

Summary of Procedure T Nodes should be placed at Discretize domain - start & end of distributed loads - point loads

Summary of Procedure For Every Element Compute Strain-Displacement Matrix B q6q6 q5q5 q4q4 q3q3 q2q2 q1q1 v u  

Summary of Procedure Element Stiffness Matrix Node Equivalent Body Force Vector Node Equivalent Traction Vector

Summary of Procedure Collect ALL Point Loads in Nodal Load Vector 1 N P x1 P y1 P xN P yN

Summary of Procedure Form Stiffness Equations

Summary of Procedure Apply Boundary Conditions Solve For Every Element Compute Stress

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

Data Processing For a given physical problem select an appropriate mathematical model e.g. Plane Stress Beam

Set Up General Model Data MaterialProperties NoNameEv  …. idBananaxxx SectionProperties NoNameAIx yy …. idApplexxx ConstantsProperties NoNameP1P2 PP …. idOrangexxx

Set Up General Model Data Element GroupsOptionsProperties NoTypeMatSecThk 11D AxialTensionid n/a 21D Axialid n/a 32D CSTPlane stressid 42D CSTPlane strainid n/a

Finite Element Mesh May be Defined in Direct Way Solid Modeling approach Nodes Elements Loads BC Geometry of Solid Loads BC Automatic Mesh Generation

Direct FEM Mesh Manually define nodes, elements, BC & loads

Direct FEM Mesh Typical Input Data (Text File or GUI) Actual depends on software

Direct FEM Mesh

Solid Modeling Describe Geometry of FE Domain as a collection of Primitive Entities Point Line Surface Volume

Solid Modeling Point Do not confuse with FEM node Line Any two points define a line Points belong to line

Solid Modeling Surface Any closed loop of lines define surface Points belong to lines Points AND lines belong to surface 2 faces are defined

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

Solid Modeling Boolean Operations Primitive Entities can be used to form more complex solid geometries

Solid Modeling Boolean Operations

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

Solid Modeling Loads and Boundary Conditions can now be applied on primitive objects regardless of the specific Finite Elements.

Automatic Meshing Structured Mesh (Mapped) Free Mesh Based on Geometric Transformations Triangulation Techniques Solid Model

Structured Mesh Transformation Through Shape Functions Map to Parent

Structured Mesh

Free Mesh Triangulation Technique Suitable for arbitrary geometries

Example Using ANSYS thickness=1” 10” 5” Plane Stress With Thickness E=29x10 6

Define Element Groups

Define Element Options

Define Thickness

Define Material

Define Key points

Defining Areas

Deleting Entities

Automatic Meshing - Coarse

Applying Boundary Conditions

Applying Loads

Positive Value Towards line

Processing…

Deformed Shape

Vertical Displacement

xx

yy

Medium Mesh

Vertical Displacement Uy = in Compare to Uy = in

 x &  y

Refine Mesh

Refined Mesh

Displacement Uy

 x &  y

Very Fine Mesh With Element Refinement

Vertical Displacement Compare to Uy = in Uy = in Uy = in

Stress Concentration

xx

yy

COMMON MISTAKES 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 Data Input

COMMON MISTAKES 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) Data Input

COMMON MISTAKES 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 Results appear correct

COMMON MISTAKES Element may be defined twice Results appear correct