Carl M. Andersen

Computerized symbolic manipulation in structural mechanics—Progress and potential

Abstract Status and recent applications of computerized symbolic manipulation to structural mechanics problems are summarized. The applications discussed include; (a) generation of characteristic arrays of finite elements; (b) evaluation of effective stiffness and mass coefficients of continuum models for repetitive lattice structures; and (c) application of Rayleigh-Ritz technique to free vibration analysis of laminated composite elliptic plates. The major advantages of using computerized symbolic manipulation in each of these applications are outlined. A number of problem areas which limit the realization of the full potential of computerized symbolic manipulation in structural mechanics are examined and some of the means of alleviating them are discussed.

Power Series Expansions for the Frequency and Period of the Limit Cycle of the Van Der Pol Equation

A power series expansion in the damping coefficient a is developed for the frequency

Perturbation analysis of the limit cycle of the free van der Pol equation

\nu ( \varepsilon )

Analysis of beam-like lattice trusses

of the limit cycle of the van der Pol equation

COMPUTERIZED SYMBOLIC MANIPULATION IN NONLINEAR FINITE ELEMENT ANALYSIS

\ddot U + U = \varepsilon \dot U( 1 - U^2 )( 0\leqq \varepsilon < \infty )

Mixed isoparametric finite element models of laminated composite shells

. The expansion is computed to

A hybrid perturbation Galerkin technique with applications to slender body theory

O( \varepsilon ^{24} )

Mixed models and reduction techniques for large-rotation nonlinear problems

in rational arithmetic using the MACSYMA symbolic manipulation system and to

Mixed isoparametric elements for saint-venant torsion

O( \varepsilon ^{164} )

Reduced basis technique for nonlinear vibration analysis of composite panels

in floating-point arithmetic using FORTRAN.A Pade analysis of the power series expansion indicates that the singularities in the complex-