A Student’s Guide to Stability Analysis of Elastic Structures with MSC Patran/Nastran and Abaqus CAE

This book is written to present both theoretical concepts of stability theory and practical techniques of stability analysis of elastic structures with the use of general-purpose finite element analysis (FEA) software packages MSC Nastran (with Patran graphical user interface) and Abaqus (with Abaqus CAE graphical user interface). The book addresses dynamic and static stability, bifurcation, critical load, postcritical deformation, instability in presence of initial deformation, analysis of thin beam based on equations of motion and equilibrium obtained with the use of simplifying assumptions on through-thickness variation of displacements, and analysis of thick and thin plates in cylindrical bending without such simplifying assumptions. The book begins by presenting basic ideas of stability of both discrete systems and continuous elastic structures and providing analytical solutions to some typical stability problems. These analytical solutions allow readers to see implementations of the general concepts and methods, and to verify the Nastran and Abaqus results obtained later for the same problems. The following portion of the text is dedicated to tutorials that demonstrate how to utilize MSC Patran/Nastran and Abaqus CAE to solve problems of stability of elastic structures. These tutorials are designed for beginners, showing step-by-step procedures of setting up models and interpreting results. An Appendix on extrema of functions and functionals is introduced into the text to help in understanding methods of applying criteria of stability and instability based on minima and maxima of total potential energy. This book is intended for students who are familiar with theory of elasticity. Read more