Zginanie sprężystej powłoki w kształcie paraboloidy eliptycznej podpartej na żebrach

Bending problem is considered of an elastic, shallow, thin shell in the form of an elliptic paraboloid, stretched over a square and supported on elastic ribs. A point of departure constitutes system of three differential equations in terms of displacements, known from the technical shell theory of V. Z. Vlasov [1]. In order to obtain a solution satisfying the boundary conditions the method of finite Fourier transform has been applied. The problem has been reduced to the solution of an infinite system of algcbraic equations. The unknowns in the system are the coefficients of the expansion of the displacements on the shell boundary in to the single Fourier series and the horizontal corner reaction. Numerical examples of displacements and internal forces have been computed for a shell loaded uniformly. The results have been compared with those obtained by numerical methods (finite differences and finite elements).