On sensitivity analysis of long piles embedded in clayey and sandy soil

The paper contains theoretical formulation of sensitivity analysis of structural systems for continuous distribution of the design variables. The functional of arbitrary component of static or kinematic field is defined with aid of Dirac delta function. The state equations of the system are connected with the functional of interest by means of Lagrange multipliers vector. The obtained differential equation with respect to Lagrange multipliers vector defines the behaviour of the adjoint structure. The components of Lagrange multipliers vector represent the constitutive equations for the adjoint structure as well as information on the type of kinematic or static unit distortions required to be imposed on the adjoint structure. The final forms of sensitivity equations are expressed by means of generalized lateral displacements for primary and adjoint structures. These equations are used in investigations of some numerical examples of practical importance.