Sensitivity Analysis and Shape Optimization of a Hole in a Vibrating Rectangular Plate for Eigenfrequency Maximization

AbstractA hole inside a rectangular thin plate is optimized for maximization of an eigenfrequency of the structure. The shape of the hole is represented by an ellipse parametrization to guarantee a smooth curve along the boundary; and the hole’s center position, semiaxes, and rotation are treated as shape design variables. The Rayleigh-Ritz approach is applied to constitute the vibration frequency equation such that an exact procedure can be presented for the frequency sensitivity analysis. The hole shape optimization is performed by using a combined mathematical programming algorithm with different search directions for two sets of design variables in relation to the constraint of the hole’s size. In addition, a simple optimality criterion is provided for the optimum profile design of the internal hole of a given area. Several illustrative examples demonstrate the validity and effectiveness of the design sensitivity analysis and the proposed optimization method.

[1]  Z. Wu.  Optimal hole shape for minimum stress concentration using parameterized geometry models , 2009 .

[2]  Sang-Bo Han,et al.  Free vibration analysis of rectangular plate with a hole by means of independent coordinate coupling method , 2007 .

[3]  E. Schnack,et al.  A new optimality criteria method for shape optimization of natural frequency problems , 2006 .

[4]  R. Haftka,et al.  Review of options for structural design sensitivity analysis. Part 1: Linear systems , 2005 .

[5]  Niels Leergaard Pedersen,et al.  An optimality criterion for shape optimization in eigenfrequency problems , 2005 .

[6]  P.A.A. Laura,et al.  Transverse vibrations of simply supported rectangular plates with two rectangular cutouts , 2003 .

[7]  K. M. Liew,et al.  Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method , 2003 .

[8]  C. Wang,et al.  Optimal location of a cutout in rectangular Mindlin plates for maximum fundamental frequency of vibration , 2002 .

[9]  Claude Fleury,et al.  A unified parametric design approach to structural shape optimization , 1995 .

[10]  Rama B. Bhat,et al.  Vibration Of Plates With Cut-Outs Using Boundary Characteristic Orthogonal Polynomial Functions In The Rayleigh-ritz Method , 1994 .

[11]  R. Haftka,et al.  Structural shape optimization — a survey , 1986 .

[12]  R. Bhat.  Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method , 1986 .

[13]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[14]  Arthur W. Leissa,et al.  The free vibration of rectangular plates , 1973 .