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

1 2

3q6

q5

q4

q3

q2

q1

vu

Summary of Procedure

V

Te dVDBBk

•Element Stiffness Matrix

•Node Equivalent Body Force Vector

•Node Equivalent Traction Vector

Summary of Procedure

Collect ALL Point Loads in Nodal Load Vector

yN

xN

y

x

y

x

P

P

P

P

P

P

2

2

1

1

P

1

N

Px1

Py1

PxN

PyN

Summary of Procedure

Form Stiffness Equations

e

ekK

PTfF e

ee

nT qqq 21Q

nT FFF 21F

KQF

Summary of Procedure

eeee qBDσ

KQF Apply Boundary Conditions

Solve FKQ 1

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 StressBeam

Set Up General Model DataMaterial Properties

No Name E v ….

id Banana xxx xxx xxx xxx

Section Properties

No Name A Ix y ….

id Apple xxx xxx xxx xxx

Constants Properties

No Name P1 P2 P ….

id Orange xxx xxx xxx xxx

Set Up General Model Data

Element Groups Options 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

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

Nodal Coordinates

No x y z ndof bc1 bc2 … bcndof

1 0.00000 1.00000 0.00000 2 1 12 1.00000 0.00000 0.00000 3 0 0 0...n xn yn zn nd x x x

Element Designation

No Mat# Sec# nnel i1 i2 i3 … innel

1 1 1 3 1 2 32 1 1 3 3 2 5...

n matn secn nneln i1n i2n i3n …

Direct FEM Mesh

Load InformationNodes

No Fx Fy Fz Mx My Mz1 1 1 3 1 2 32 1 1 3 3 2 5...n

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”

10”

5”

5”

Plane Stress

With Thickness

E=29x106

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

Applying Loads

Positive Value

Towards line

Processing…

Deformed Shape

Vertical Displacement

x

y

Medium Mesh

Vertical Displacement

Uy = 0.002042 in

Compare to

Uy = 0.001905 in

x & y

Refine Mesh

Refined Mesh

Displacement Uy

x & y

Very Fine Mesh With Element Refinement

Vertical Displacement

Compare to

Uy = 0.002042 in

Uy = 0.001905 in

Uy = 0.002084 in

Stress Concentration

Stress Concentration

x

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