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

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

Peridynamics topology optimization of three-dimensional structures with surface cracks for additive manufacturing

Additive manufacturing (AM) is an effective approach to fabricating intricate shapes obtained from topology optimization (TO). However, it may cause undesired manufacturing-induced defects/cracks due to high thermal residual stresses. This study proposes a PeriDynamics-enabled three-dimensional Topology Optimization method (PD-TO) for designing structures by considering surface cracks for the AM processes. The PD-TO approach employs a bi-directional evolutionary structural optimization method and uses particle discretization of geometry for mechanical analysis. Crack surfaces are generated by breaking three-dimensional nonlocal interactions of the particles, and thus, during the optimization process, complex multiple structural discontinuities can be diligently modeled. First, the proposed approach is validated by solving benchmark problems without cracks. For each benchmark geometry, the PD-TO analysis is then performed by considering different positions and numbers (single/multiple) of cracks. These analyses extensively investigate and demonstrate the effects of a priori knowledge of residual stress-induced damages/cracks on the optimum topology for additive manufacturing. Besides, the smoothing operation is applied to the optimum designs to transform voxel shapes into AM-friendly smooth surfaces. These geometries are manufactured by an extrusion-based AM process to demonstrate the practical engineering application of the proposed method. Finally, the comparison of numerical results is also supported by the experimental tests conducted on the optimized topologies. Overall, it is confirmed that the PD-TO approach is a viable and accurate optimization tool for additive manufacturing considering possible process-induced damages

Continuous density-based topology optimization of cracked structures using peridynamics

Peridynamics (PD) is a meshless approach that addresses some of the difficulties and limitations associated with mesh-based topology optimization (TO) methods. This study investigates topology optimization of structures with and without embedded cracks using peridynamics (PD-TO). To this end, PD is coupled with two different continuous density-based topology optimization methods, namely the optimality criteria and the proportional optimization. The optimization results are compared for a continuous definition of the design variables,which are the relative densities defined for PD particles. The checkerboard issue has been removed using filtering schemes. The accuracy of the proposed PD-TO approach is validated by solving benchmark problems and comparing the optimal topologies with those obtained using a FEM-based topology optimization. Various problems are solved with and without defects (cracks) under different loading and constraint boundary conditions. Topology optimization for an unstructured discretization problem has also been investigated applied to a complex geometry. The optimal topology of a cracked structure may change for different optimization methods. The numerical results demonstrate the accuracy, high efficiency, and robustness of the PD-TO approach