Dynamic fracture analysis of plates loaded in tension and bending using the dual boundary element method

© 2020 Trans Tech Publications Ltd, Switzerland. The purpose of this paper is to solve dynamic fracture problems of plates under both tension and bending using the boundary element method (BEM). The dynamic problems were solved in the Laplace-transform domain, which avoided the calculation of the domain integrals resulting from the inertial terms. The dual boundary element method, in which both displacement and traction boundary integral equations are utilized, was applied to the modelling of cracks. The dynamic fracture analysis of a plate under combined tension and bending loads was conducted using the BEM formulations for the generalized plane stress theory and Mindlin plate bending theory. Dynamic stress intensity factors were estimated based on the crack opening displacements

Lightning strike simulation in composite structures

Lighting strike is one of the critical threats to the safety of composite aircrafts during flight. This work reports on numerical simulation of lightning strike in composite structures. Different modelling techniques using the commercial software ABAQUS, together with damage models are studied to find the most appropriate one in comparison to experimental results. Once the numerical model is validated, the effect of insertion of carbon nanotubes (CNTs) and metallic mesh in the composite is investigated. It is concluded that inserting CNTs in the top layer of the composite can improve its lightning strike protection noticeably

Statistical Inference of Equivalent Initial Flaw Size Distribution for Fatigue Analysis of an Anisotropic Material

A novel methodology for the fatigue life uncertainty quantification of anisotropic structures is presented in this work. The concept of the equivalent initial flaw size distribution (EIFSD) is employed to overcome the difficulties in small cracks detection and fatigue prediction. This EIFSD concept is combined with the dual boundary element method (DBEM) to provide an efficient methodology for modelling the fatigue crack growth. Bayesian inference is used to infer the EIFSD based on inspection data from the routine maintenance of the structure, simulated with the DBEM. A large amount of DBEM simulations were required for the Bayesian inference. Therefore, surrogate models are used as part of the inference to further improve computational efficiency. A numerical example featuring an anisotropic plate is investigated for demonstrating the proposed methodology. When considering a low level of uncertainty in the crack propagation parameters, an error of 0.12% was found between the estimated fatigue life obtained using the proposed method compared to actual fatigue life, and only 0.35% error when considering high level of uncertainty. The application of the estimated fatigue life can be used to determine an appropriate inspection interval for aircraft maintenance

Numerical modelling of 2D woven composites by the projective element method

A novel method is presented in this paper to allow for realistic creation of 2D woven composite fabric models considering deformation modes incurred during manufacturing. The proposed computational framework is named as the Projective Element Method (PEM). The PEM provides a new strategy for the woven composite modelling, in which a representative numerical model for woven composites is built based on the well-distributed projective lines along the out-of-plane direction of the composites structure. The developed model is simplified yet accurate particularly for the 2D woven composites and can perform the compaction simulations in seconds and the results obtained are comparable to the finite element simulation which requires hours or even days of computation. The comparison between the PEM results and the real material is also presented with the micro-images obtained experimentally, thus further validating the proposed method

Probabilistic multi-scale design of 2D plain woven composites considering meso-scale uncertainties

This paper presents a novel multi-scale design strategy for 2D plain woven composites considering the manufacturing process. The design methodology integrates the meso-structural geometry of woven fabric composites to maximise the buckling load of composite stiffened panels at the macro-level. A numerical model to simulate the autoclave manufacturing process of woven composites is developed, in which a new geometric modelling method is proposed to construct a more realistic RVE model for 2D plain woven composites accounting for the compaction effects. Deterministic and robust design optimisations are conducted to find solutions with both high performances and high robustness to uncertainties. In particular, this study considers the morphological uncertainties of the meso-scale fabric structure, i.e. yarns’ waviness and porosity incurred during manufacturing and its influence on the structural integrity of the parts. The optimisation results obtained from the deterministic and robust design problems are presented. A parametric analysis is conducted to characterise the sensitivity of the fabric properties to the geometry of yarns and related uncertainties. It is shown that the space between yarns has a significant negative impact on the structural buckling load and negative impact on the cure-induced residual stresses

Smart patch repair with low profile PVDF sensors

Bonded repair of composite structures still remains a major concern for the airworthiness authorities because of the uncertainty about the repair quality. This work, investigates the applicability of conventional Structural Health Monitoring (SHM) techniques for monitoring of bonded repair with ring-shaped low profile sensors. A repaired composite panel has been sensorized with two Ring-Shaped Polyvinylidene fluoride piezopolymer Sensors (RSPS) and a piezoelectric (PZT) transducer. An electromechanical impedance (EMI) and Lamb wave analysis have been carried out to check the sensitivity of these sensors to detect an artificially introduced damage simulating a disbond of the repair. The state of the repair have been successfully monitored and reported by both methods

Damage detectability model of pitch-catch configuration in composite plates

Detectability of damage using Lamb waves depends on many factors such as size and severity of damage, attenuation of the wave and distance to the transducers. This paper presents a detectability model for pitch-catch sensors configuration for structural health monitoring (SHM) applications. The proposed model considers the physical properties of lamb wave propagation and is independent of damage detection algorithm, which provides a generic solution for probability of detection. The applicability of the model in different environmental and operational conditions is also discussed

Spectral BEM for the Analysis of Wave Propagation and Fracture Mechanics

This paper presents a spectral boundary element formulation for analysis of structures subjected to dynamic loading. Two types of spectral elements based on Lobatto polynomials and Legendre polynomials are used. Two-dimensional analyses of elastic wave propagation in solids with and without cracks are carried out in the Laplace frequency domain with both conventional BEM and the spectral BEM. By imposing the requirement of the same level of accuracy, it was found that the use of spectral elements, compared with conventional quadratic elements, reduced the total number of nodes required for modeling high-frequency wave propagation. Benchmark examples included a simple one-dimensional bar for which analytical solution is available and a more complex crack problem where stress intensity factors were evaluated. Special crack tip elements are developed for the ¯rst time for the spectral elements to accurately model the crack tip ¯elds. Although more integration points were used for the integrals associated with spectral elements than the conventional quadratic elements, shorter computation times were achieved through the application of the spectral BEM. This indicates that the spectral BEM is a more e±cient method for the numerical modeling of structural health monitoring (SHM) processes, in which high-frequency waves are commonly used to detect damage, such as cracks, in structures

Reliability-based fracture analysis for plate bending problems with the dual boundary element method

A novel methodology is presented for the efficient reliability analysis of plate structures containing cracks with the Dual Boundary Element Method (DBEM). The derivatives of the DBEM plate formulations for the Crack Surface Displacement Extrapolation (CSDE) method have been derived for the first time and are used as part of an Implicit Differentiation Method (IDM) for the efficient calculation of Stress Intensity Factor (SIF) sensitivities. A numerical example is investigated in which results from the presented CSDE methodology are compared to those from the J-integral. The SIF sensitivities were used with the First-Order Reliability Method (FORM) to determine the reliability of a plate structure containing a crack. Results indicate that the proposed CSDE methodology is capable of providing estimates for reliability that are very similar to those provided by the J-integral. Given that the proposed CSDE methodology can be easier to implement, it could prove to be an effective alternative to the J-integral for the efficient reliability analysis of plate structures containing cracks

Modelling of the high-frequency fundamental symmetric Lamb wave using a new boundary element formulation

This paper presents a new boundary element formulation for modelling the fundamental symmetric Lamb wave (S0 mode) propagating in the high frequency range. At such high frequencies, the S0 mode reveals significant dispersive character. Conventional BEM formulations governed by the generalised plane stress theory fail to accurately represent the dispersive properties of the S0 mode and to handle out-of-plane loads because the effects of thickness-stretch are not considered. Therefore, a new BEM formulation is proposed based on the dynamic fundamental solutions which are derived for the first time for a higher-order plate theory (Kane–Mindlin) taking into account coupling between extensional motion and the first mode of thickness vibration. Only plate edges are required to be discretized using simple line elements in the proposed BEM formulation. Three benchmark examples are presented where the solutions from the new BEM formulation are shown to be in excellent agreement with analytical and three-dimensional finite element results. Furthermore, the advantage of the proposed formulation is demonstrated through comparisons with the BEM results based on the generalised plane stress theory