THE BIHARMONIC BOUNDARY VALUE PROBLEM AS APPLIED TO A MEMBRANE HAVING IRREGULAR SHAPE.
OKLAHOMA STATE UNIV STILLWATER SCHOOL OF MECHANICAL ENGINEERING
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A two-dimensional linear elastostatic boundary value problem is formulated for a web having irregular shape. The stresses in the interior of the region are found by obtaining the Airy function then taking second partial derivatives. Finite-difference numerical techniques used by British authors are used except that the simultaneous equations are solved directly instead of using relaxation methods. With the aid of the irregular biharmonic star operator, the equations are written in matrix notation and solved with digital computing equipment. An aluminum alloy semi-monocoque shell structure, fitted with electric resistance strain gages, is loaded statically. Data taken from these experiments are compared to the theoretical values. Ancillary information involving ultrasonic, optical, photostress, and brittle lacquer experiments are briefly described. A coarse 1 in square and a fine 12 in square grid was formulated for two variations of slope equations. Theoretical-to-experimental stress comparison show nearly perfect agreement for centrally located nodes for all 4 variations of theory. Maximum dispersion occurs in sigma sub yy at the boundary adjacent to the vertical shear load transfer member. Author
- Structural Engineering and Building Technology