A Review and Study on Ritz Method Admissible Functions with Emphasis on Buckling and Free Vibration of Isotropic and Anisotropic Beams and Plates

On the application of the Ritz method to free vibration and buckling analysis of highly anisotropic plates

“…The efficiency of the present Ritz approach can be observed by the maximum time taken for an analysis using 100 shape functions along both the directions, approximately equal to 0.75 s. Conversely, the results reported in Ref. [23] using modified characteristic functions (MCF) and orthogonal polynomials (OP) require computational times which are several order of magnitudes higher. This discrepancy, partly due to the smaller amount of RAM memory used in the computations of Ref.…”

“…Given the efficiency of the proposed implementation, it is interesting to provide an insight into the computational time required by typical calculations. A comparison is presented against the results of Moreno-Garcia et al [23], where computational times are reported for different sets of shape functions. A fully clamped isotropic plate is taken as a benchmark; dimensions and material properties are those of Ref.…”

“…A fully clamped isotropic plate is taken as a benchmark; dimensions and material properties are those of Ref. [23]. The time needed to extract the first ten frequencies is reported in Fig.…”

“…This discrepancy, partly due to the smaller amount of RAM memory used in the computations of Ref. [23], is believed to be mainly motivated by the analytical . Table 8 Percent number of not-null terms in the stiffness matrix using analytical and numerical integration; ED 332 theory, 30 × 30 functions.…”

“…A comprehensive recent review regarding the admissible functions used in the Ritz method is available in Ref. [23], where focus is given on thin isotropic plates. Merits and demerits of six sets of functions are discussed and compared in terms of convergence, computational time and numerical stability.…”