Finite Element Procedures

) (structure):

- .- . - .- .

) (structure):

) (Structural Analysis)

- . .- .

) (structure):

) (Structural Analysis)

) :

1- (Stress, strain and deflection characteristics under static or quasi-static loading or deformation conditions)2- (Vibrational response characteristics under dynamic loading conditions)3- (Buckling characteristics under static or dynamic loading conditions) : : (Dynamics of structures) : (Stability of structures)

) (structure):

) (Structural Analysis)

) :) (Structural Design):

- - (stable) (resistant-with strength) (efficient) (Economical) (aesthetical) (safe).- .

) (structure):

) (Structural Analysis)

) :) (Structural Design):

. - . ) (Structural Idealization) (Mathematical Modeling)

- (Real structure) .- .- . . . (concept of Hierarchy)- .

: - - -

: - - ( )

- 1955-1945 :) .) ( 1940)- (Applied Mathematics) . 1940 (Moment Distribution) .

- . - (Matrix Algebra) .- .- : ( ) ( )- (optimization) (Material and Geometic Nonlinearity) .

- : ) (Framed structures) . ( ).

- : ) (Framed structures) ) (Mass structures) ( ...).

- : ) (Framed structures) ) (Mass structures) ) (Shell structures) (Membrane structures) ( ..).

- : ) (Framed structures) ) (Mass structures) ) (shell structures) (Membrane structures) ) ( )

- ( ) . ( )

- (skeletal structures) (continuum structures) .- .

) (Small Displacement Theory)

) (Linear Behavior of Material)

- (yield point) .

Geometric Nonlinearity Material Nonlinearity.

* (principle of superposition) . .

) (Principle of Equilibrium)

( ). ( ) :

1- (Equilibrium of structure) . :

2- (Equilibrium of Node)- .Pi : (Generalized Forces) iPij: i ij

3- (Equilibrium of Member) :Pij : i ijPji : j ij: . hji

) (Principle of Compatibility)

. . :1) - - .2) . (Rigid) . (i) i . :ij : i ij- (Semi-Rigid) (Frictionless pin) .

) (External work)- .- (P ) . v . :- :- (Generalized displacements and forces) . () () :

- :

) ( )- . ( ) . - . . .

:

i,i .- :

- (i=Ei,): -

- :

:

* ( L):

* ( L):

* : ( L)

* : ( L)

) (Principle of Virtual work)- .- (Rigid body) (Deformable body) ( ) :1- : .- .

Qi: Q Vi: Vi= V0

2- : Q Q Q .

(External virtual work) (Internal virtual work)Virtual strain corresponding to virtual displacementReal stress in equilibrium withReal applied load

) (Theorems of Castiliano) .- : ( ) ( ) .- : ( ) ( ) .

- Pi i . - .

- (Stiffness Coefficients) ( ):

* L F ( u ).

( Axial Stiffness: EA/L) .

* L T ( ).

( Torsional Stiffness: GJ/L) .

) (Bettis Law) (Maxwells Reciprocal Relationship) .

1) : Pm Pn (mn) Pn Pm (nm) .

- :

2) : .- m P n n P m ( ).

. . ( (Equilibrium Method) ). . ( (Compatibility Method) ). . ( ) ( ) . ( + ). (Degree of Freedom).

- . (6) x,y (3) (3) x,y (2) (0) (3) (1) (2) (0) (1)

- :1) 2) 3) 4) 5) .

( ) (Stiffness method) (Equilibrium method) (Displacement method) .

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