Solution of three-dimensional problems of elasticity theory using new formulas for harmonic polynomials

Approximate solutions of three-dimensional problems of elasticity theory ar e sought in the form of linear combinations of vector functions each of whi ch satisfies a differential equation. The linear-combination coefficients a re found by energy minimization of the difference between exact and approxi mate solutions. This can be realized in the first and second basic problems . Simple recursion relations and differentiation formulas for similar harmo nic polynomials are obtained. The above mentioned vector functions are cons tructed using these formulas and the Trefftz representation, The problem of a truncated pyramid is considered.