Sensitivity Analysis of a CPAM Inverse Algorithm for Composite Laminates Characterization

Abstract

Using experimental data and numerical simulations, a new combined technique is presented for characterization of thin and thick orthotropic composite laminates. Four or five elastic constants, as well as ply orientation angles, are considered as the unknown parameters. The material characterization is first examined for isotropic plates under different boundary conditions to evaluate the method's accuracy. The proposed algorithm, so-called CPAM (Combined Programs of ABAQUS and MATLAB), utilizes an optimization procedure and makes simultaneous use of vibration test data together with their corresponding numerical solutions. The numerical solutions are based on a commercial finite element package for efficiently identifying the material properties. An inverse method based on particle swarm optimization algorithm is further provided using MATLAB software. The error function to be minimized is the sum of squared differences between experimental and simulated data of eigenfrequencies. To evaluate the robustness of the model's results in the presence of uncertainty and unwanted noises, a sensitivity analysis that employs Gaussian disorder model is directly applied to the measured frequencies. The results with high accuracy confirm the validity and capability of the present method in simultaneous determination of mechanical constants and fiber orientation angles of composite laminates as compared to prior methods.

Identification of mechanical and damage parameters of composite laminates based on a CPAM method

“…According to the fourth constraint of relation (8), E1 should be randomly generated between E2 and the upper limit of E1. Moreover, it is also confirmed by the previous study 1 that to estimate the amount of υ12 reasonably, it would be better than its value generated according to the third constraint of relation (8). For damage parameters, first, values of its position ( X 0 and Y 0 ) are randomly generated inside the plates.…”

“…It means that data space is larger than the size of the model space. 1 The proposed inverse method utilizes the experimental natural frequencies and mode shapes for the determination of the four and five mechanical properties and also the damage parameters. Also, because the inverse solution can determine the model space correctly, the first two conditions are satisfied well and the problem would be well-posed to identify the parameters of the inverse problem.…”

“…This optimization cycle should be so repeated between this two software that optimizes the error function. How these algorithms work is explained here step by step 1 to expose a better understanding of this procedure. Furthermore, the corresponding flowchart of this algorithm is represented in Figure 2.…”

“…Because natural frequencies obtained experimentally, are independent of position and rigidities of these strings, boundary conditions of these plates are considered completely free. 1,5…”

“…As an example, this vibrational data for composite plates can be obtained from mechanical properties and dimensional data of damage area. As it has been followed in the previous study, 1 an available commercial finite element code can be used for un-damped free vibration modeling of plates.…”