The Moment Finite-Element Scheme in Problems of Nonlinear Continuum Mechanics

The conceptual and theoretical fundamentals of the original moment finite-element scheme (MFES) developed to solve problems of nonlinear continuum mechanics are presented. Typical examples of model problems are given to illustrate the advantages of the MFES over other traditional finite-element schemes. The basic relationships for studying the nonlinear deformation and distortion of mechanical continuum systems are formulated in an invariant tensor form. Also, some mathematical algorithms specially developed to solve systems of nonlinear equations of high order are described. The numerical solutions obtained are proved reliable and rapidly converging to the exact solutions for a sufficient number of test problems. Results of strength, postbuckling stability, vibration, fracture, and high-speed influence analyses of real mechanical systems are illustrated.