Structural health monitoring of marine structures by using inverse finite element method

A new state-of-the art methodology named as inverse Finite Element Method (iFEM) is adopted to solve the inverse problem of real-time reconstruction of full-field structural displacements, strains, and stresses. iFEM has shown to be precise, robust, and fast enough to reconstruct the three dimensional displacement field of structures in real-time by utilizing surface strain measurements obtained from strain sensors embedded on the structure. The numerical implementation of the iFEM methodology is done by considering four-node inverse quadrilateral shell element. Two demonstration cases are presented including a quadrilateral plate subjected to bending force and a stiffened plate under bending loading. Finally, the effect of sensor locations, number of sensors and the discretization of the geometry are examined on solution accuracy

Determination of horizon size in state-based peridynamics

Peridynamics is based on integro-differential equations and has a length scale parameter called horizon which gives peridynamics a non-local character. Currently, there are three main peridynamic formulations available in the literature including bond-based peridynamics, ordinary state-based peridynamics and non-ordinary state-based peridynamics. In this study, the optimum horizon size is determined for ordinary state-based peridynamics and non-ordinary state-based peridynamics formulations by using uniform and non-uniform discretisation under dynamic and static conditions. It is shown that the horizon sizes selected as optimum sizes for uniform discretisation can also be used for non-uniform discretisation without introducing significant error to the system. Moreover, a smaller horizon size can be selected for non-ordinary state-based formulation which can yield significant computational advantage. It is also shown that same horizon size can be used for both static and dynamic problems

A peridynamic based machine learning model for one-dimensional and two-dimensional structures

With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics based machine learning model for one and two-dimensional structures. The linear relationships between the displacement of a material point and displacements of its family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction for a plate with a pre-existing crack, a two-dimensional representation of a three-point bending test, and a plate subjected to dynamic load are simulated

Free and forced vibration analysis of piezolaminated plates via an isogeometric layerwise finite element

Isogeometric layerwise finite element (L-IGA) formulation is a recent state-of-the-art approach integrating Non-Uniform Rational B-spline (NURBS) basis functions into the quasi-static solution process of piezolaminated composite plates. This study extends the application of the L-IGA framework to encompass free, forced vibration, and displacement control analyses of laminated composite plates with straight/curvilinear fibers and piezoelectric layers. To this end, the NURBS basis functions, utilized in geometry definition, are employed to solve electromechanically coupled differential equations following Hamilton’s variational principle. The adoption of high-order continuous NURBS shape functions throughout the IGA discretization span both in-plane and through-thickness laminate dimensions. This effectively facilitates precise geometry representation directly from Computer-Aided Design (CAD). Besides, such a discretization accelerates the convergence of displacement and electric potential solution fields toward exact results. Various benchmark problems have been solved to verify the robustness and high accuracy of the proposed dynamic L-IGA method. These include comparative analyses between L-IGA dynamic solutions (i.e. employing the Newmark-Beta method), analytical solutions, and ANSYS-Solid 226 finite element results. All the results are compared across various span-to-thickness ratios, mechanical-potential loading scenarios, and fiber orientation angles. Remarkably, the L-IGA method attains almost excellently accurate time response of various fields (displacement, stress, electric potential) and modal results, with considerably fewer mesh elements than Solid 226 solutions. Overall, such an outcome reveals the high potential and practical merits of the proposed L-IGA formulation as a proficient finite element approach for the dynamic analysis of piezolaminated plates

A novel isogeometric layerwise element for piezoelectric analysis of laminated plates with straight/curvilinear fibers

This study presents an isogeometric layerwise element, L-IGA based on the principle of virtual displacement theory to model the bending behavior of laminated smart composite plates integrated with piezoelectric layers. Instead of using Lagrangian or Hermitian type polynomials encountered in standard finite element technology, L-IGA utilizes high-order Non-Uniform Rational B-Splines (NURBS) functions for both in-plane and through-the-thickness discretization of the geometry and the kinematic variables. Additionally, it allows different numbers of NURBS degrees and elements to be used for each patch through the thickness of the plate. In this way, exact geometry, and highly accurate solutions with rapid convergence for the benchmark electromechanical problems in the literature have been guaranteed by using L-IGA analysis. The precision of the results is meticulously verified by 3-D Ansys SOLID226 finite elements and analytical solutions. Thus, the L-IGA element can be adopted for computationally efficient and accurate static analysis of laminated plates having straight/curvilinear fibers for piezoelectric actuator and sensor configurations

A novel delamination damage detection strategy based on inverse finite element method for structural health monitoring of composite structures

In recent years, structural health monitoring (SHM) has been revolutionized with the advent of the inverse finite element method (iFEM), which is a superior sensing technology based on the minimization of a weighted least squares error functional between experimental and numerical strain measures. This approach is suitable for damage detection thanks to its highly accurate and full-field displacement reconstruction capability within the physical domain of the structure. This study focuses on the development of a novel damage detection strategy for identifying internal/external defect types in composites, e.g., delamination, surface debonding, etc., by utilizing iFEM. The core formulation is derived by employing the kinematic relations of the refined zigzag theory (RZT) within the iFEM framework. By utilizing the field variables achieved via the iFEM-RZT, equivalent von Mises strains are computed for individual plies. After that, through the definition of various damage indices, the health of the structure is evaluated in terms of the presence of damage as well as its extent and through-the-thickness position and in-plane size of the damage in laminated composite materials. Various case studies with different damage scenarios are simulated for the assessment of iFEM-RZT capability in terms of shape-sensing and SHM. As a result, the inverse algorithm shows its remarkable efficiency and accuracy in detecting flawed regions over the problem domain and through the thickness of layered materials, both in terms of the location of the damage as well as its morphology

Implementation of shear-locking-free triangular refined zigzag element for structural analysis of multilayered plates with curvilinear fibers

Modeling and analysis of composites with curvilinear fiber reinforcement is rather challenging in terms of accuracy and computational cost associated with variable material stiffness. In this study, to reduce the computational cost drastically without sacrificing the numerical accuracy, variable stiffness composite laminate (VSCL) is modelled as a single layer based on the refined zigzag theory (RZT). To this end, a three-node triangle RZT element formulation is adopted and effectively implemented for static analysis of multilayer composites and sandwich plates with curvilinear fiber paths. Moreover, to accurately model the strains in VSCL, the derivatives of the zigzag functions with respect to planar coordinates are considered for each ply within the laminate in the RZT kinematic-strain relations. Enhanced capability of the present model is verified by performing comprehensive numerical investigation on several benchmark cases. The obtained results are compared with those present in the literature and three-dimensional elasticity solutions. Hence, it is demonstrated that the triangular RZT element is a fast, robust, and accurate structural analysis platform that can potentially lend itself to the optimization of curvilinear fiber angles of VSCL

Damage growth and failure detection in hybrid fiber composites using experimental in-situ optical strain measurements and smoothing element analysis

In previous study the failure initiation and development in hybrid fiber laminates was successfully monitored and determined. In current investigation a novel damage monitoring approach is proposed for hybrid laminates by combining different optical strain measurement techniques namely digital image correlation (DIC), fiber Bragg grating sensors (FBG) and infrared thermography (IRT) with smoothing element analysis (SEA). This viable experimental procedure eliminates the effects of global/local nature of optical strain measurement systems on heterogeneous damage accumulation and is a two-step approach. First, all optical sensing systems together with conventional strain gauges are utilized concurrently to indicate the differences in the measured strains and monitor damage accumulation under tensile loading. This demonstrates how failure events disturb the measurement capabilities of optical systems, which can cause a miscalculation of hybrid effect in hybrid-fiber laminates. The second step involves the utilization of SEA algorithm for discretely measured DIC displacements to predict a realistic continuous displacement/strain map and rigorously mitigate the inherent noise of the full field optical system. Remarkably, for large deformation states in hybrid composites, the combination of SEA/DIC enables early prediction of susceptible damage zones at stress levels 30% below material strength