Push Bound

George Trapp and Bohe Wang

Computer Science and Electrical Engineering Department,
West Virginia University, Morgantown WV 26506

Abstract

The push bound problem is a very interesting one. When we push at a plate, sometime all plate goes ahead, sometime some place bounds. C. V. Coffman and R. J. Duffin[1], R. J. Duffin[2] and P. R. Garabedian[3] did good job in this field. Here, what we are considering is, for square plates, when we push at a given point, which points will bound. Using difference method and MATLAB, we deal with common material (like galss, steel, ...) and composite material square plates. The position where the load P acts on is from corner to center. The results are shown in case 1 and case 2.

Case 1. Common Material Push Bound

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

 

Case 2. Composite Material Push Bound

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

 

References

[1] C. V. Coffman and R. J. Duffin, On the structure of biharmonic functions satisfying the clamed plate conditions on a right angle, Adv. In appl. Math. 1(1980), 373-389.

[2] R. J. Duffin, Some problems of mathematics and science, Bull Amer. Math. Soc. 80(1974), 1053-1070.

[3] P. R. Garabedian, A Partial Differential Equation arising in Conformal Mapplig, Pacific J. Math 1(1951), 485-524