In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least s...In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least squares(IMLS)method,which enhances the efficiency and stability of the numerical solution.The numerical solution formulas are derived using the improved element-free Galerkin(IEFG)method.We introduce the solid isotropic microstructures with penalization(SIMP)model to formulate a mathematical model for topology opti-mization,which effectively penalizes intermediate densities.The optimization problem is defined with the numerical solution formula and volume fraction as constraints.The objective function,which is the minimum value of flexibility,is optimized iteratively using the optimization criterion method to update the design variables efficiently and converge to an optimal solution.Sensitivity analysis is performed using the adjoint method,which provides accurate and efficient gradient information for the optimization algorithm.We validate the proposed framework through a series of numerical examples,including clamped beam,cantilever beam,and simply supported beam made of orthotropic materials.The convergence of the objective function is demonstrated by increasing the number of iterations.Additionally,the stability of the iterative process is analyzed by examining the fluctuation law of the volume fraction.By adjusting the parameters to an appropriate range,we achieve the final optimization results of the IEFG method without the checkerboard phenomenon.Comparative studies between the Element-Free Galerkin(EFG)and IEFG methods reveal that both methods yield consistent optimization results under identical parameter settings.However,the IEFG method significantly reduces computational time,highlighting its efficiency and suitability for orthotropic materials.展开更多
A low-frequency multi-mode ultrasonic Lamb wave method suitable for character- izing the thickness, the density and the elastic constants of the ultra-thin transversely isotropic laminate composite is presented. The &...A low-frequency multi-mode ultrasonic Lamb wave method suitable for character- izing the thickness, the density and the elastic constants of the ultra-thin transversely isotropic laminate composite is presented. The 'ultra-thin' here means that the thickness of the plate is much less than the wavelength of the ultrasonic wave so that the echoes from the front and back faces of the plate can't be separated in the time domain. The dispersion equations for the low frequency ultrasonic Lamb waves with the propagation directions parallel and vertical to the fiber direction are derived. In conjunction with the least square algorithm method, the secant algorithm is used to estimate the parameters of the ultra-thin fiber-reinforced composite layer. The evaluation errors and the sensitivity of the method to different paramters of the thin composite are analyzed. The technique has been used to characterize the ultra-thin grass fiber reinforced PES composite with thickness down to ten percents of the ultrasonic wavelength. It is observed that the agreement between the nominal and the estimation values is reasonably good.展开更多
基金supported by the Graduate Student Scientific Research Innovation Project through Research Innovation Fund for Graduate Students in Shanxi Province(Project No.2024KY648).
文摘In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least squares(IMLS)method,which enhances the efficiency and stability of the numerical solution.The numerical solution formulas are derived using the improved element-free Galerkin(IEFG)method.We introduce the solid isotropic microstructures with penalization(SIMP)model to formulate a mathematical model for topology opti-mization,which effectively penalizes intermediate densities.The optimization problem is defined with the numerical solution formula and volume fraction as constraints.The objective function,which is the minimum value of flexibility,is optimized iteratively using the optimization criterion method to update the design variables efficiently and converge to an optimal solution.Sensitivity analysis is performed using the adjoint method,which provides accurate and efficient gradient information for the optimization algorithm.We validate the proposed framework through a series of numerical examples,including clamped beam,cantilever beam,and simply supported beam made of orthotropic materials.The convergence of the objective function is demonstrated by increasing the number of iterations.Additionally,the stability of the iterative process is analyzed by examining the fluctuation law of the volume fraction.By adjusting the parameters to an appropriate range,we achieve the final optimization results of the IEFG method without the checkerboard phenomenon.Comparative studies between the Element-Free Galerkin(EFG)and IEFG methods reveal that both methods yield consistent optimization results under identical parameter settings.However,the IEFG method significantly reduces computational time,highlighting its efficiency and suitability for orthotropic materials.
基金the National Natural Science Foundation of China (No. 69631020) and theOffice of Naval Research of America (00014-93-1-0340).
文摘A low-frequency multi-mode ultrasonic Lamb wave method suitable for character- izing the thickness, the density and the elastic constants of the ultra-thin transversely isotropic laminate composite is presented. The 'ultra-thin' here means that the thickness of the plate is much less than the wavelength of the ultrasonic wave so that the echoes from the front and back faces of the plate can't be separated in the time domain. The dispersion equations for the low frequency ultrasonic Lamb waves with the propagation directions parallel and vertical to the fiber direction are derived. In conjunction with the least square algorithm method, the secant algorithm is used to estimate the parameters of the ultra-thin fiber-reinforced composite layer. The evaluation errors and the sensitivity of the method to different paramters of the thin composite are analyzed. The technique has been used to characterize the ultra-thin grass fiber reinforced PES composite with thickness down to ten percents of the ultrasonic wavelength. It is observed that the agreement between the nominal and the estimation values is reasonably good.
