| Title |
Relationships between Generalized Functions and Influence Functions |
| Authors |
Kwak Soon-Seop ; Song Kil-Ho |
| Keywords |
Generalized Functions ; Influence Function ; Green Function ; Muller-Breslau's Principle ; Double Moment ; Double Shear ; Unit Force ; Unit Moment ; Unit Deflection Angle Discontinuity ; Unit Deflection Discontinuity |
| Abstract |
This study analyses the relationship between Generalized Functions and influence functions in Winkler base. Muller-Breslau's principle is difficult for getting the exact value in influence lines at which we are concerned. But the meaning of this principle can be expressed in terms of the Generalized Functions in governing differential equations, EIy''''+ky=q, and due to the very convenient characteristics of the Generalized Functions in q, we can get the particular solutions of the D.E. easily. The conclusion are followings 1) The influence functions for the deflection, deflection angle, moment and shear at ξ when unit force is applied at x, are the deflections which is the solutions in EIy''''+ky=q, when the qs are expressed in terms of the δ0,δ-1,EIδ-2,EIδ-3 respectively. 2) The influence functions for the deflection, deflection angle, moment and shear at ξ when unit moment is applied at x are those deflections which are the solution in EIy''''+ky=q when the qs are expressed in terms of the -δ-1,δ-2,-EIδ-3,-kδ0 respectively. 3) The influence functions for the deflection, deflection angle, moment and shear at ξ when unit deflection angle discontinuity is applied at x are those deflections which are the solutions in D.E. when the qs are expressed in terms of the EIδ-2,EIδ-3,-kEIδ0,-kEIδ-1 respectively. 4) For the case of unit deflection discontinuity is applied at x, we get the influence functions for the deflection, deflection angle, moment and shear at ξ from the solutions of D.E. where q is expressed in terms of -EIδ-3,-kδ0,kEIδ-1,-kEIδ-2 respectively. Here we can see the rotation of δ0,δ-1,δ-2,δ-3 depending on the cases of loads in q. |