Abstract
A new and effective elastic constants identification technique is presented to extract the elastic constants of a composite laminate subjected to uniaxial tensile testing. The proposed technique consists of a new multi-level optimization method that can solve different types of minimization problems, including the extraction of material constants of composite laminates from given strains. In the identification process, the optimization problem is solved by using a stochastic multi-start dynamic search minimization algorithm at the first level in order to obtain the statistics of the quasi-optimal design variables for a set of randomly generated starting points. The statistics of the quasi-optimal elastic constants obtained at this level are used to determine the reduced feasible region in order to formulate the second-level optimization problem. The second-level optimization problem is then solved using the particle swarm algorithm in order to obtain the statistics of the new quasi-optimal elastic constants. The iteration process between the first and second levels of optimization continues until the standard deviations of the quasi-optimal design variables at any level of optimization are less than the prescribed values. The proposed multi-level optimization method, as well as several existing global optimization algorithms, is used to solve a number of well-known mathematical minimization problems to verify the accuracy of the method. For the adopted numerical examples, it has been shown that the proposed method is more efficient and effective than the adopted global minimization algorithms to produce the exact solutions. The proposed method is then applied to identify four elastic constants of a [0°/±45°]s composite laminate using three strains in 0°, 45°, and 90° directions, respectively, of the composite laminate subjected to uniaxial testing. For comparison purposes, several existing global minimization techniques are also used to solve the elastic constants identification problem. Again, it has been shown that the proposed method is capable of producing more accurate results than the adopted available methods. Finally, experimental data are used to demonstrate the applications of the proposed method.
Highlights
As is well known, the determination of the true elastic constants is an essential step for design, fabrication, and the structural health monitoring of structures
Most of the previously proposed vibration-based elastic constants identification techniques used a number of measured, structural natural frequencies to formulate the minimization problem, which is solved by using a minimization algorithm to determine the material constants
The above constrained optimization problem is first converted to the unconstrained minimization problem, as stated in Equation (2) and the M sets of K particles that were randomly generated in the feasible region of this level were used in the particle swarm optimization technique (PSOT) to search for the global minimum
Summary
The determination of the true elastic constants is an essential step for design, fabrication, and the structural health monitoring of structures. The uncertainties of, for instance, the measured modal characteristics, the mathematical model for analyzing composite plate vibration, modeling the actual boundary conditions, etc., may significantly affect the accuracy of the identified elastic constants At this stage, the techniques of using vibration data for elastic constants identification of composite materials/structures may not be completely viable for practical applications. Without the need to perform any full-field measurements, Kam and his associates [12,17,18,19] used optimization methods and measured strains/displacements at some particular points on composite plates to identify the elastic constants of the constituent composite materials. The search for simple testing procedures and for the accurate identification of elastic constants, for engineering applications, still remains an important topic of research To tackle this problem, Kam and his associates [17,18,19]. The accuracy and feasibility of the proposed method to identify elastic constants of different composite materials are studied by way of several numerical and experimental examples
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