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3 . H o w e v e r , a s s o o n a s i n c r e m e n t a l l o a d i n g p r o c e d u r e w a s e m p l o y e d w i t h t h e stiffness m a t r i x r e c a l c u l a t e d in e a c h s t e p , t h i s t e n d e n c y f a d e d o u t a n d a d i f f e r e n t c o n f i g u r a t i o n s h o w n in F i g . 4 w a s obtained which unquestionably resembles better the real tire d e f o r m a t i o n . T h i s is b e c a u s e t h e c o r d p a n t a g r a p h c h a n g e s its 656 Y . 00 Y Fig. 3. Tire deformation for 29 psi inflation load, linear analysis.

M o r e specifically, o u r o b j e c tive w a s t o p r o v i d e a n e l e m e n t t h a t c a n be e m p l o y e d e c o n o m i c a l l y t o m o d e l assemblages of pipe b e n d s a n d s t r a i g h t s for n o n l i n e a r s t a t i c a n d d y n a m i c a n a l y s e s . C o n s i d e r i n g the analysis limitations of the element, it w o u l d b e p o s s i b l e t o e x t e n d t h e r a n g e o f a p p l i c a b i l i t y , b u t s u c h r e f i n e m e n t s m u s t b e c h o s e n in a v e r y careful m a n n e r a n d with considerable ingenuity so as n o t to u n d u l y increase the complexity a n d cost of the element.

1. Precast hollow-core slabs. T h i s t y p e o f e l e m e n t h a s b e e n u s e d in t h e p a s t in a m o r e specific f o r m u l a t i o n in R e f s . [ 1 , 2, 5] for t h e solution of c o n t a c t p r o b l e m s . T o analyse the stress tResearch Assistant. ^Professor. §Doctor of Eng. Sciences. 669 670 M . KEUSER et ai t r a n s f e r in p r e s t r e s s e d tie b a c k s a b o n d - l i n k e l e m e n t w a s p r e s e n t e d in Ref. [8]. ( 1 ) General formulation In o r d e r t o a c h i e v e c o m p a t i b i l i t y w i t h t h e e l e m e n t s a v a i l a b l e in A D I N A , b o n d is m o d e l l e d b y a f o u r node contact element with a linear displacement formulation.

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