Prediction of the spring-in of cylindrically orthotropic media and cross-ply laminates

The equation for prediction of the spring-in angle of a cylindrically orthotropic segment is shown to be independent of all material properties except for the anisotropic coefficients of thermal expansion and a stress-free state is insured for the corresponding unconstrained deformation. In contrast, the complete cylindrical geometry is shown to provide constraint to thermal deformation and thereby induce thermal residual stresses in the form of a moment. The method of superposition is demonstrated whereby traction-free conditions yield stress-free cylindrical elements with corresponding angular displacements at the element free boundaries. The first derivation of the spring-in equation is attributed to Radford, in contrast to the widely accepted view that the equation was first developed by Spencer et al. Finite-element methods, combined with the superposition approach, further validate the accuracy of the Radford equation for cylindrically orthotropic segments and explore its limitations for multiaxial composite laminates.

Model parameterization and amplitude variation with angle and azimuthal inversion in orthotropic media

Horizontal layered formations with a suite of vertical or near-vertical fractures are usually assumed to be an approximate orthotropic medium and are more suitable for estimating fracture properties with wide-azimuth prestack seismic data in shale reservoirs. However, the small contribution of anisotropic parameters to the reflection coefficients highly reduces the stability of anisotropic parameter estimation by using seismic inversion approaches. Therefore, a novel model parameterization approach for the reflectivity and a pragmatic inversion method are proposed to enhance the stability of the inversion for orthotropic media. Previous attempts to characterize orthotropic media properties required using four or five independent parameters. However, we have derived a novel formulation that reduces the number of parameters to three. The inversion process is better conditioned with fewer degrees of freedom. An accuracy comparison of our formula with the previous ones indicates that our approach is sufficiently precise for reasonable parameter estimation. Furthermore, a Bayesian inversion method is developed that uses the amplitude variation with angle and azimuth (AVAZ) of the seismic data. Smooth background constraints reduce the similarity between the inversion result and the initial model, thereby reducing the sensitivity of the initial model to the inversion result. Cauchy and Gaussian probability distributions are used as prior constraints on the model parameters and the likelihood function, respectively. These ensure that the results are within the range of plausibility. Synthetic examples demonstrate that the adopted orthotropic AVAZ inversion method is feasible for estimating the anisotropic parameters even with moderate noise. The field data example illustrates the inversion robustness and stability of the adopted method in a fractured reservoir with a single well control.

Extended meshless moving Kriging method for crack propagation analyzing in orthotropic media

Orthotropic composite material is the particular type of anisotropic materials and their products have been extensively used in a wide range of engineering applications. Study on mechanical behaviors of such materials under working conditions is very essential. In this study, an extended meshfree moving Kriging interpolation method (namely as X- MK) is presented for crack analyzing in 2D orthotropic materials models. The Gaussian function is used for constructing the moving Kriging shape functions. Typical advantages of the MK shape function are the high-order continuity and the satisfaction of the Kronecker’s delta property. To calculate the stress intensity factors (SIFs), interaction integral method is used with orthotropic auxiliary fields. Several numerical tests including static SIFs calculating and crack propagation predicting are performed to verify the accuracy of the present approach. The obtained results are compared with available refered results and they have shown a very good performance of the present method.

Identification of conductivity in inhomogeneous orthotropic media

Purpose The purpose of this paper is to solve numerically the identification of the thermal conductivity of an inhomogeneous and possibly anisotropic medium from interior/internal temperature measurements. Design/methodology/approach The formulated coefficient identification problem is inverse and ill-posed, and therefore, to obtain a stable solution, a non-linear regularized least-squares approach is used. For the numerical discretization of the orthotropic heat equation, the finite-difference method is applied, while the non-linear minimization is performed using the MATLAB toolbox routine lsqnonlin. Findings Numerical results show the accuracy and stability of solution even in the presence of noise (modelling inexact measurements) in the input temperature data. Research limitations/implications The mathematical formulation uses temporal temperature measurements taken at many points inside the sample, and this may be too much information that is provided to identify a space-wise dependent only conductivity tensor. Practical implications As noisy data are inverted, the paper models real situations in which practical temperature measurements recorded using thermocouples are inherently contaminated with random noise. Social implications The identification of the conductivity of inhomogeneous and orthotropic media will be of great interest to the inverse problems community with applications in geophysics, groundwater flow and heat transfer. Originality/value The current investigation advances the field of coefficient identification problems by generalizing the conductivity to be anisotropic in addition of being heterogeneous. The originality lies in performing, for the first time, numerical simulations of inversion to find the orthotropic and inhomogeneous thermal conductivity from noisy temperature measurements. Further value and physical significance are brought in by determining the degree of cure in a resin transfer molding process, in addition to obtaining the inhomogeneous thermal conductivity of the tested material.