VARIATIONAL CALCULUS, ENERGY THEOREMS, SAINT-VENANT'S PRINCIPLE

The following sections are included:

• MINIMIZATION OF FUNCTIONALS

• FUNCTIONAL INVOLVING HIGHER DERIVATIVES OF THE DEPENDENT VARIABLE

• SEVERAL UNKNOWN FUNCTIONS

• SEVERAL INDEPENDENT VARIABLES

• SUBSIDIARY CONDITIONS — LAGRANGIAN MULTIPLIERS

• NATURAL BOUNDARY CONDITIONS

• THEOREM OF MINIMUM POTENTIAL ENERGY UNDER SMALL VARIATIONS OF DISPLACEMENTS

• EXAMPLE OF APPLICATION: STATIC LOADING ON A BEAM—NATURAL AND RIGID END CONDITIONS

• THE COMPLEMENTARY ENERGY THEOREM UNDER SMALL VARIATIONS OF STRESSES

• VARIATIONAL FUNCTIONALS FREQUENTLY USED IN COMPUTATIONAL MECHANICS

• SAINT-VENANT'S PRINCIPLE

• SAINT-VENANT'S PRINCIPLE — BOUSSINESQ–VON MISES–STERNBERG FORMULATION

• PRACTICAL APPLICATIONS OF SAINT-VENANT'S PRINCIPLE

• EXTREMUM PRINCIPLES FOR PLASTICITY

• LIMIT ANALYSIS