A PROGRAM FOR SOLVING 1D ELASTOSTATIC PROBLEM: A BAR OF UNIT LENGTH SUBJECTED TO

LINEAR BODY FORCE. THE LEFT END OF THE BAR IS FIXED AND THE RIGHT FREE.



THE ANALYTICAL SOLUTION IS GIVEN BY

u = (x/2 - x\^3/6)/E

WHERE X REPRESENTS THE COORDINATE ALONG THE BAR AND E IS THE ELASTIC MODULUS

IN THE COMPUTATION, THE INTEGRAL IS CALCULATED OVER THE SUBDOMAIN THUS THE BACKGROUND

CELLS FOR INTEGRATION ARE NO LONGER REQUIRED.



THE PENALTY METHOD IS EMPLOYED TO ENFORCE THE ESSENTIAL BOUNDARY CONDITIONS

-A PROGRAM FOR SOLVING 1D ELASTOSTATIC PROBLEM: A BAR OF UNIT LENGTH SUBJECTED TO

　　　　　 LINEAR BODY FORCE. THE LEFT END OF THE BAR IS FIXED AND THE RIGHT FREE.



　　　　　 THE ANALYTICAL SOLUTION IS GIVEN BY

　　　　　　　 u = (x/2 - x\^3/6)/E

　　　　　 WHERE X REPRESENTS THE COORDINATE ALONG THE BAR AND E IS THE ELASTIC MODULUS

　　　　　 IN THE COMPUTATION, THE INTEGRAL IS CALCULATED OVER THE SUBDOMAIN　THUS THE BACKGROUND

　　　　　 CELLS FOR INTEGRATION ARE NO LONGER REQUIRED.



　　　　　 THE PENALTY METHOD IS EMPLOYED TO ENFORCE THE ESSENTIAL BOUNDARY CONDITIONS