Application of the method of split rigidities to anisotropic laminated shallow shells

In this paper, according to the method stated by Hu Haichang in [3], on the basis of [1], the method of split rigidities is generalized for the purpose of solving the problems of lateral deflection, stability and lateral vibration for anisotropic laminated shallow shells, and a simple and practical approximate method is obtained, in which the errors and computing work are comparatively small.     

A series boundary integration method for the bending analysis of anisotropic plates

A series boundary integration method is given which exactly satisfies the fundamental equation of bending analysis of general anisotropic plates or laminated plates in Kirchhoffs sense. With a unified deflection series, the method may be applied to the plates having different planforms and support conditions. Several groups of representative examples are calculated. The examples include circular, square and triangular plates, and their boundaries include clamped edges, simply supported edges, free edges and free corner. Numerical results indicate rapid convergency for both deflection and stress resultants and demonstrate wide applicability of the method.This subject was supported by the Natural Science Foundation of Guangdong Province.     

Thermal bending analysis of shear-deformable laminated anisotropic plates by the GDQ method

The generalized differential quadrature (GDQ) method was used to determine the inter-laminar stresses and deflections in a laminated rectangular anisotropy plate under thermal bending involving the effect of shear deformation. We obtained the non-dimensional stresses and transverse center deflection in cross-ply and angle-ply anti-symmetric, anisotropic laminates subjected to thermal load with sinusoidal temperature distribution. We found that the shear deformation has significant effects on the stresses and deflections for laminated anisotropic plate with moderately side-to-thickness ratio under thermal load and bending state.     

Green’s-function method for modeling surface acoustic wave dispersion in anisotropic material systems and determination of material parameters

A Green’s-function method for modeling propagation of surface acoustic waves in anisotropic nanolayered materials is reviewed. The mathematical model, developed at NIST, provides a computationally efficient inversion algorithm for determination of the material parameters of the film, such as its elastic constants and density, from observed dispersion of the surface acoustic waves. The application of the method to a 306 nm thick TiN film having transverse isotropy on a single crystal Si substrate is discussed as an example. The errors in the values of the parameters determined by using the inversion algorithm and the question of uniqueness of the values of the parameters are discussed in detail. It is suggested that, at least in the example considered in this paper, the SAW dispersion can be used to determine any two parameters of the film, provided other parameters are known by independent measurements. In particular, the values of c₁₁ and the density of the film, obtained from the measured SAW dispersion, are the most reliable and the value of c₄₄ is the least reliable. The method is extended to account for defective bonding between the film and the interface and the effect of an intermediate layer of silica between the film and the substrate.     

Extension of the virtual fields method to elasto-plastic material identification with cyclic loads and kinematic hardening

The virtual fields method (VFM) has been specifically developed for solving inverse problems from dense full-field data. This paper explores recent improvements regarding the identification of elasto-plastic models. The procedure has been extended to cyclic loads and combined kinematic/isotropic hardening. A specific attention has also been given to the effect of noise in the data. Indeed, noise in experimental data may significantly affect the robustness of the VFM for solving such inverse problems. The concept of optimized virtual fields that minimize the noise effects, previously developed for linear elasticity, is extended to plasticity in this study. Numerical examples with models combining isotropic and kinematic hardening have been considered for the validation. Different load paths (tension, compression, notched specimen) have shown that this new procedure is robust when applied to elasto-plastic material identification. Finally, the procedure is validated on experimental data.     

Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains. To realize this method, we design a new wavelet basis function, by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains. In the solution of differential equations, various derivatives of the unknown function are denoted as new functions. Then, the integral relations ...     

Characterization of material mechanical properties using strain correlation method combined with virtual fields method

Acta Mechanica Sinica - The isotropic and anisotropic behaviors are considered as the important formats of the constitutive behaviors, and can also be called the global properties. To improve the...     

Application of the virtual fields method to mechanical characterization of elastomeric materials

This paper deals with the identification of constitutive parameters of a Mooney model suitable for hyperelastic materials. These parameters are retrieved from a multiaxial mechanical test that gives rise to heterogeneous stress/ strain fields. Since no analytical relationship is available between measurements and unknown parameters, a suitable tool, namely the virtual fields method, is developed in case of large deformations and used to identify these unknowns. Several results obtained with numerical simulations and experiments performed on rubber specimens illustrate the approach.     

Constitutive parameters identification of thermal barrier coatings using the virtual fields method

Thermal barrier coatings (TBCs) are widely applied in thermal components to protect metallic components. Owing to the complex layered structure of TBCs and difficult preparation of coating, the mechanical characterization of TBCs should be of primary importance. With regard to TBCs, this study deals with the constitutive parameters identification of bi-material. Considering the complex construction and boundary of bi material, the virtual fields method (VFM) was employed in this study. A methodology based on the optimized virtual fields method combined with moire interferometry was proposed for the constitutive parameters identification of bi-material. The feasibility of this method is verified using simulated deformation fields of a two-layer material subjected to three point ben ding loading. As an application, the deformation fields of the TBC specimens were measured by moire interferometry. Then, lhe mechanical parameters of the coating were identified by the proposed method. The identification results indicate that Young's modulus of the TBC top coating is 89.91 GPa, and its Poisson's ratio is 0.23.     

Isotropicalized spline integral equation method for the analysis of anisotropic plates

In the view of Reissner’s and Kirchhoff’s theories,respectively,we formulate theisotropicalized governing equations for the anisotropic plates,and give the proof of theequivalence relation between these two plate-models for the simply-supported rectangularorthotropic plates.The well-known fundamental solutions of the isotropic plates are utlizedfor the spline integral equation analysis of anisotropic plates.Even with sparse meshes thesatisfactory results can be obtained.The analysis of plates on two-parameter elasticfoundation is so simple as the common case that only a few terms should be added to theformulas of fictitious loads.     

A finite difference method at arbitrary meshes for the bending of plates with variable thickness

A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper.The method is completely general with respect to various boundary conditions,load cases and shapes of plates.This difference scheme is simple and the numerical results agree well with those obtained by other methods.     

Reciprocal theorem method for solving the problems of bending of thick rectangular plates

ＲＥＣＩＰＲＯＣＡＬＴＨＥＯＲＥＭＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＥＰＲＯＢＬＥＭＳＯＦＢＥＮＤＩＮＧＯＦＴＨＩＣＫＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＳＦｕＢａｏ－ｌｉａｎ（付宝连）Ｔａｎｗｅｎ－ｆｅｎｇ（谭文锋）（ＹａｎｓｈａｎＵｎｉｒｅｒｓｉｔ...     

功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。     

A method using the reciprocal theorem to solve the bending of thin elastic semicircular plates

The bending of the thin elastic semicircular plates, because of its complicated boundary conditions, brings some difficulties for us to obtain its solution. This paper applies the reciprocal theorem to propose a general simple convenient method to obtain the transverse defiectional equations of the plates.     

Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effects

Based on the Reddy ‘s theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature ( DQ ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert ( DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.