FREE VIBRATION AND BUCKLING ANALYSIS OF HIGHLY SKEWED PLATES BY LEAST SQUARES-BASED FINITE DIFFERENCE METHOD

It is well-known that stress singularities occur at the obtuse corners of skew plates, especially when the skew angles are large. Owing to the stress singularities, accurate bending results, vibration frequencies and buckling loads of highly skewed plates are difficult to obtain accurately. In this paper, the mesh-free least squares-based finite difference (LSFD) method is proposed for solving the free vibration and buckling problems of highly skewed plates. As such vibration and buckling results are scarce in the open literature, the method was verified by comparing the LSFD solutions with existing ones having a skew angle θ ≤ 70°, or by carrying out convergence studies. The vibration and buckling results for plates with very large skew angle (θ = 80°) are presented for the first time. The close agreement observed in the comparison studies and the good convergence behavior of the LSFD solutions provide the confidence that these vibration and buckling results predicted by the LSFD method are of good accuracy.

Accurate Vibration Analysis of Simply Supported Rhombic Plates by Considering Stress Singularities

This is the first known work which explicitly considers the bending stress singularities that occur in the two opposite, obtuse corner angles of simply supported rhombic plates undergoing free, transverse vibration. The importance of these singularities increases as the rhombic plate becomes highly skewed (i.e., the obtuse angles increase). The analysis is carried out by the Ritz method using a hybrid set consisting of two types of displacement functions, e.g., (1) algebraic polynomials and (2) corner functions accounting for the singularities in the obtuse corners. It is shown that the corner functions accelerate the convergence of solution, and that these functions are required if accurate solutions are to be obtained for highly skewed plates. Accurate nondimensional frequencies and normalized contours of the vibratory transverse displacement are presented for simply supported rhombic plates with skew angles ranging to 75 deg. (i.e., obtuse angles of 165 deg.). Frequency and mode shapes of isosceles and right triangular plates with all edges simply supported are also available from the data presented.

Analysis of Combined Pressure-Shear Waves in an Elastic/Viscoplastic Material

A numerical solution is presented for the case of symmetric impact of two skewed plates, modeled to represent 6061-T6 Aluminum. The main features of the solution are, except near the impact face, the same as in previous solutions based on a rate-independent theory. Free-surface velocity-time profiles are obtained for the target rear surface. These profiles indicate that the fine structure of the normal velocity should be resolvable by means of a laser velocity-interferometer.