The engineering community generally accepts that there exists only a small set of closed-form solutions for simple cases of bars, beams, columns, and plates. Despite the advances in powerful computing and advanced numerical techniques, closed-form solutions remain important for engineering; these include uses for preliminary design, for evaluation
Foreword. Prologue. Introduction: Review of Direct, Semi-Inverse and Inverse Eigenvalue Problems. Unusual Closed-Form Solutions in Column Buckling. Unusual Closed-Form Solutions for Rod Vibrations. Unusual Closed-Form Solutions for Beam Vibrations. Beams and Columns with Higher-Order Polynomial Eigenfunctions. Influence of Boundary Conditions on Eigenvalues. Boundary Conditions Involving Guided Ends. Vibration of Beams in the Presence of an Axial Load. Unexpected Results for a Beam on an Elastic Foundation or with Elastic Support. Non-Polynomial Expressions for the Beam's Flexural Rigidity for Buckling or Vibration. Circular Plates. Epilogue. Appendices. References. Author Index. Subject Index.