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TALLER 03ELEMENTOS FNITOS

ELEMENTOS EN 2D

OSCAR FERNANDO GARCIA GUARDO

ING. CIVIL

MSC. ING. CIVIL - GEOTECNIA

UNIVERSIDAD DEL NORTE

DOCENTE.

Dr. WILLIAM FUENTES LACOUTUCRE

FECHA

15-06-16

BARRANQUILLA ATLANTICO

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Solucion Ejercicio 1.

+ = 022 + 22 + = 0 + + = 0Haciendo

1 =

2 =

1 + 2 + = 0De la integracin por partes

() = +

() = + = ()

1 = 1 +1

1

=

1

1

2 = 2 + 2 2 = 2 2

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Reemplazando.

1

+

2

2

1 +

= 0

1 + 2

2 + 1 = 0

1 (1) = 0

2 (2) = 0

(1) 1 + 2

2 +

= 0

1 2 + + 1 + 2 = 0

1 2 + + = 0

+ + = 0

7/25/2019 Solucion Taller Oscar Garcia Guardo

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Discretizacin.

, , = (, )

=1

= (, )=1

=1

=1

+

=1 + = 0

+

=1 + = 0

=1 =

=1 = +

=

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Fuente. An Introduction to the finite element method

J.N-Reddy

Matrices de rigides elemntos rectagulares.

= 116

2 2 1 12 2 1 111

11 22 22 +22

6 2 1 1 21 2 2 112 21 21 12

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Ejericio 2.

Matris de rigides global.

K=

Nodos Conocidos

1,2,3,4,5,6

Nodos desconocidos

7,8,9,10,11,12,13,14,15

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Condensando

K11=

K12=

=2

22

00

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Resolviendo queda

1 =22 =23 =24 =05 =0

6 =1.87 = 1.78 =1.39 =0.910 =0.6

11 = 1.912 =1.713 =1.314 =0.915 =0.8