Li Ming Zhou

A Cell-Based Smoothed XFEM for Fracture in Piezoelectric Materials

This paper presents a cell-based smoothed extended finite element method (CS-XFEM) to analyze fractures in piezoelectric materials. The method, which combines the cell-based smoothed finite element method (CS-FEM) and the extended finite element method (XFEM), shows advantages of both methods. The crack tip enrichment functions are specially derived to represent the characteristics of the displacement field and electric field around the crack tip in piezoelectric materials. With the help of the smoothing technique, integrating the singular derivatives of the crack tip enrichment functions is avoided by transforming interior integration into boundary integration. This is a significant advantage over XFEM. Numerical examples are presented to highlight the accuracy of the proposed CS-XFEM with the analytical solutions and the XFEM results.

Cell-Based Smoothed Finite Element Method-Virtual Crack Closure Technique for a Piezoelectric Material of Crack

In order to improve the accuracy and efficiency of solving fracture parameters of piezoelectric materials, a piezoelectric element, tailored for the virtual crack closure technique (VCCT), was used to study piezoelectric materials containing a crack. Recently, the cell-based smoothed finite element method (CSFEM) and VCCT have been used to simulate the fracture mechanics of piezoelectric materials. A center cracked piezoelectric materials with different material properties, crack length, mesh, and smoothing subcells at various strain energy release rates are discussed and compared with finite element method-virtual crack closure technique (FEM-VCCT). Numerical examples show that CSFEM-VCCT gives an improved simulation compared to FEM-VCCT, which generally simulates materials as too stiff with lower accuracy and efficiency. Due to its simplicity, the VCCT piezoelectric element demonstrated in this study could be a potential tool for engineers to practice piezoelectric fracture analysis. CSFEM-VCCT is an efficient numerical method for fracture analysis of piezoelectric materials.

Enriched Element-Free Galerkin Method for Fracture Analysis of Functionally Graded Piezoelectric Materials

A new method using the enriched element-free Galerkin method (EEFGM) to model functionally graded piezoelectric materials (FGPMs) with cracks was presented. To improve the solution accuracy, extended terms were introduced into the approximation function of the conventional element-free Galerkin method (EFGM) to describe the displacement and electric fields near the crack. Compared with the conventional EFGM, the new approach requires smaller domain to describe the crack-tip singular field. Additionally, the domain of the nodes was not affected by the crack. Therefore, the visibility method and the diffraction method were no longer needed. The mechanical response of FGPM was discussed, when its material parameters changed exponentially in a certain direction. The modified -integrals for FGPM were deduced, whose results were compared with the results of the conventional EFGM and the analytical solution. Numerical example results illustrated that this method is feasible and precise.

Analysis of Dynamic Fracture Parameters in Functionally Graded Material Plates with Cracks by Graded Finite Element Method and Virtual Crack Closure Technique

Based on the finite element software ABAQUS and graded element method, we developed a dummy node fracture element, wrote the user subroutines UMAT and UEL, and solved the energy release rate component of functionally graded material (FGM) plates with cracks. An interface element tailored for the virtual crack closure technique (VCCT) was applied. Fixed cracks and moving cracks under dynamic loads were simulated. The results were compared to other VCCT-based analyses. With the implementation of a crack speed function within the element, it can be easily expanded to the cases of varying crack velocities, without convergence difficulty for all cases. Neither singular element nor collapsed element was required. Therefore, due to its simplicity, the VCCT interface element is a potential tool for engineers to conduct dynamic fracture analysis in conjunction with commercial finite element analysis codes.

A New Response Surface Method for Structural Reliability Analysis

The response surface method is adopted to analyze the structural reliability. This paper presents a new response surface method with the uniform design method to predict the failure probability of structures. It is the response surface method based on Fourier orthogonal basis function (RSM-Fourier). To reduce computational costs in structural reliability analysis, approximate Fourier response surface functions for reliability assessment have been suggested. The method involves the selection of training datasets for establishing a model by the uniform design points, the approximation of the limit state function by the trained model and the estimation of the failure probability using first-order reliability method (FORM). The proposed method is applied to examples, compared with other methods to demonstrate its effectiveness.

Interval Perturbation Method to Structural Non-Probabilistic Reliability Analysis

In structural non-probabilistic reliability analysis, the uncertain structural parameters are assumed to be the interval parameters. The commonly used probability model will lose accuracy when there is not enough experimental date for the reliability analysis. Conversely, the interval model only requires the upper and lower bound of the uncertain variable, which is more reasonable compared with the probabilistic model. The interval perturbation method is applied in this paper to compute the non-probabilistic reliability index, where the interval expansion problem has been effectively controlled. The precision of computing the reliability index is effectively improved, solving the problem of the non-probabilistic reliability index in a new way. The numerical results prove that this method is effective and feasible.

Structural Non-Probabilistic Reliability Analysis Based on Imperialist Competitive Algorithm

A structural non-probabilistic reliability analysis model based on the imperialist competitive algorithm (ICA) is proposed. In practical engineering, the independent variables of the limit state function are usually the structural responses, which, together with the gradients, need to be resolved. The proposed model could find out the global optimum solution through the competition among the empires, without any additional gradient information, showing a good feasibility in many kinds of optimization problems. When utilizing the penalty function method, the constraint domain is enlarged to the failure domain, overcome the difficulties of searching the optimum due to the former narrower constraint domain. A numerical example verifies the high precision and good feasibility of the model.

An Inhomogeneous Cell-Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

Hybrid reliability analysis of structural fatigue life: Based on Taylor expansion method

A new method for computing the failure probability of the fatigue life is proposed, dealing with uncertain problems with both random and interval variables. Using a Taylor expansion and the concept of statistical moment, the first four central moments of the structural fatigue life performance function are obtained. Then, using a second Taylor expansion, the first four central moments are expanded at the midpoint of the interval variable, and the intervals of the statistical moments of the performance function are calculated. The obtained moment information is applied into an Edgeworth series expansion expression, giving the cumulative distribution function of the structural fatigue life performance function and getting its interval of the failure probability. Two numerical examples of growing complexity are employed to demonstrate the feasibility of the proposed approach.

A Structural Reliability Analysis Approach for Uncertain Structures via a PSO-DE Hybrid Algorithm

A structural reliability analysis approach for uncertain structures based on a PSO-DE hybrid algorithm was proposed. In order to analyze the structural non-probabilistic reliability for structures with uncertain parameters, an optimization problem by using the convex model and the penalty function method was formulated. For better convergence speed and precision, the particle swarm optimization (PSO) algorithm and the differential evolution (DE) algorithm were combined to solve the structural reliability optimization problem, this PSO-DE hybrid algorithm was based on the evolution of the cognitive experience. The numerical examples were presented to demonstrate the effectiveness and accuracy of the proposed structural reliability analysis method.