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Finite Element Method (FEM) 1

CIVL512

Finite Element Methods (FEM)

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Finite Element Method (FEM) 2

Part 1

Review of Matrix Algebra, force &

stiffness methods

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Finite Element Method (FEM) 3

Matrix Algebra

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Finite Element Method (FEM) 4

Matrix Algebra

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Finite Element Method (FEM) 5

Matrix Algebra

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Finite Element Method (FEM) 6

Matrix Algebra

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Finite Element Method (FEM) 7

Matrix Algebra

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Finite Element Method (FEM) 8

Matrix Algebra

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Finite Element Method (FEM) 9

Matrix Algebra

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Finite Element Method (FEM) 10

Matrix Algebra

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Finite Element Method (FEM) 11

Displacement and force method

Two basic solution procedures of structural

analysis Displacement method (stiffness method)

Force method (flexibility method)

Deduced from Minimum potential energy (displacement method)

Minimum complimentary potential energy (force

method) Directly from manipulating the governing system

equations (for both methods)

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Finite Element Method (FEM) 12

Force method

1. Make the structure statically determinate,or statically indeterminate if the solution

is known

2. Insert releases and insert redundant

forces that are unknowns

3. Displacements are expressed in terms offorces by means of flexibility matrices

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Finite Element Method (FEM) 13

Force method4. Insert continuity/compatibility

conditions5. Solve the resulting set of equations for

the unknown forces

Example, continuous beam

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Force method

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Force method

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Force method

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Force method

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Force method

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Force Method

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Force method

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Force method

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Force method

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Force method

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Force method

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Force method

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Force method

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Force method

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Force method

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Displacement method1. The displacement of the joints of a

structure are taken as the unknowns2. The member forces are expressed in

terms of those displacements

3. The relationship between the two is

defined by the stiffness matrix

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Finite Element Method (FEM) 30

Displacement method

Stiffness coefficients

and fixed end moments

for prismatic beams

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Displacement method Example

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Displacement method

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Displacement method

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Finite Element Method (FEM) 34

Generalized stiffness method Derive generalized beam stiffness matrix

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Generalized stiffness method

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Generalized stiffness method

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Generalized stiffness method

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Finite Element Method (FEM) 38

Generalized stiffness method

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Generalized stiffness method Example

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Finite Element Method (FEM) 40

Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method

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Stiffness method