Flamant problem plays significance in practical problems such as bridges. It is concentrated load acting on the free boundary of semi-infinite plate. Solution for flamant problem with elastic inclusion has been obtained by classical method such as involution technique. Body force method, a semi-numerical method based on principle of superposition is used to obtain solutions [1,2]. In the present work, complex potentials of involution technique for the Kelvin type problem with elastic inclusion in hole (In plane concentrated load acting in the infinite plate with elastic inclusion in hole) [3,4] is used as fundamental solution.The flamant problem with elastic inclusion in hole is shown in Fig.1.
The imaginary free boundary (AB} of infinite plate with elastic inclusion in hole acted upon by a concentrated load ‘F’ at “P” is divided into number of equal divisions as shown in Fig.2. On each division unit concentrated load in x and y directions are applied and resultant forces along each division in × and y directions are calculated due to these unit concentrated loads. The boundary conditions require that these resultant forces along each segment are nullified due to resultant forces along each segments created by concentrated load acting on the boundary. By this, the imaginary free boundary of infinte plate becomes stress free and becomes free edge of semi-infinite plate as shown in Fig,2.The body forces are calculated which are to be applied at the midpoint of each divisions. Now the free boundary becomes stress free and it is equivalent to flamant problem with elastic inclusion in hole. Hoop stresses, radial stresses and tangential stresses are calculated around the hole and compared with involution technique. It is found that the results are more closure to involution technique.
