Linear programming and limit analysis of shell roofs

Limit analysis for cylindrical shell roofs has been formulated as a linear programming problem based on lower bound theorem. The differential equations of equilibrium for a circular cylindrical shell element are transformed into algebraic equations by finite differences. The equilibrium equations and the linearized non-linear yield conditions at various points of the shell are linear functions of the stress resultants. These form the linear constraints of the problem. The load parameter is taken as an objective function and it is maximized using revised simplex method. For a shell of given geometry, stress resultants at various points are obtained to give the optimum collapse load. Thus the versatile technique avoids various trial solutions to achieve best lower bound for complicated shell problems.