Displacement and stress monitoring of a Panamax containership using inverse finite element method

The inverse Finite Element Method (iFEM) is a revolutionary methodology for real - time reconstruction of full-field structural displacements and stresses in plate and shell structures that are instrumented by strain sensors. This inverse problem is essential for structural health monitoring systems and commonly referred as ‘displacement and stress monitoring’ or ‘shape-and stress-sensing’. In this study, displacement and stress monitoring of a Panamax containership is performed based on the iFEM methodology. A simple, efficient, and practically useful four-node quadrilateral inverse-shell element, iQS4, is used for the numerical implementation of the iFEM algorithm. Hydrodynamic analysis of the containership is performed for beam sea waves in order to calculate v ertical and horizontal wave bending moments, and torsional wave moments acting on parallel mid-body of the containership. Several direct FEM analyses of the parallel mid-body are performed using the hydrodynamic wave bending and torsion moments. Then, experimentally measured strains are simulated by strains obtained from high-fidelity finite element solutions. After that, three different iFEM case studies of the parallel mid-body are performed utilizing the simulated sensor strains. Finally, the effect of sensor locations and number of sensors are assessed with respect to the solution accuracy

Shape sensing of aerospace structures by coupling of isogeometric analysis and inverse finite element method

This paper presents a novel isogeometric inverse Finite Element Method (iFEM) formulation, which couples the NURBS-based isogeometric analysis (IGA) together with the iFEM methodology for shape sensing of complex/curved thin shell structures. The primary goal is to be geometrically exact regardless of the discretization size and to obtain a smoother shape sensing even with less number of strain sensors. For this purpose, an isogeometric KirchhoffLove inverse-shell element (iKLS) is developed on the basis of a weighted-least-squares functional that uses membrane and bending strain measures consistent with the KirchhoffLove shell theory. The novel iKLS element employs NURBS not only as a geometry discretization technology, but also as a discretization tool for displacement domain. Therefore, this development serves the following beneficial aspects of the IGA for the shape sensing analysis based on iFEM methodology: (1) exact representation of computational geometry, (2) simplified mesh refinement, (3) smooth (high-order continuity) basis functions, and finally (4) integration of design and analysis in only one computational domain. The superior capabilities of iKLS element for shape sensing of curved shells are demonstrated by various case studies including a pinched hemisphere and a partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined

Displacement and stress monitoring of a chemical tanker based on inverse finite element method

Real-time reconstruction of full field structural displacements, strains, and stresses by using surface strain measurements obtained from on-board strain sensors is commonly referred to as shape- and stress-sensing. For this purpose, a computationally accurate, robust, and rapid algorithm named as inverse Finite Element Method (iFEM) was recently developed. The main goal of this study is to perform displacement and stress monitoring of a typical chemical tanker mid-ship based on iFEM methodology. The numerical implementation of the iFEM algorithm is done by considering four-node inverse quadrilateral shell (iQS4) element. In order to demonstrate the capability of the current approach, a long barge that has a cross-section identical to a typical chemical tanker is modeled with iQS4 elements. Then, hydrodynamic loads of the barge for a certain frequency of waves are calculated by using in-house hydrodynamic software. Then, these forces are applied to a FEM model of barge and structural response is computed by using in-house finite element software. The results obtained from FEM analysis is utilized as a source to simulate in-situ strain data used in iFEM analysis as input. Finally, iFEM and FEM displacements are compared and the effects of locations and number of sensors on iFEM solution accuracy are discussed

Isogeometric iFEM analysis of thin shell structures

Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated

Electromechanical contact elements for modelling adhesion and interfacial interactions in electrospun nanofibers systems

Abstract The analysis of deformation and interactions during the electromechanical contact between surfaces with non-matching meshes is important for advanced applications such as mechanical energy harvesting and pressure/force sensors using flexible piezoelectric devices made of polymeric nanowires. The node-to-segment (NTs) and the node-to-surface (NTS) algorithms are widely employed discretization techniques despite well known limitations in problems where the identification of the master segment/surface related to a slave-node is ambiguous or impossible. The objectives of this work is to extend the classical formulation to electromechanical interfaces using automatic differentiation technologies to derive and implement the resulting numerical equations. In particular, the contact contributions to the stiffness matrix and to the residual vector are derived and an adhesion behaviour is also added into the constitutive law. Then, some applications to selected practical problems are presented

A comparative and review study on shape and stress sensing of flat/curved shell geometries using C0-continuous family of iFEM elements

In this study, we methodologically compare and review the accuracy and performance of C0-continuous flat and curved inverse-shell elements (i.e., iMIN3, iQS4, and iCS8) for inverse finite element method (iFEM) in terms of shape, strain, and stress monitoring, and damage detection on various plane and curved geometries subjected to dierent loading and constraint conditions. For this purpose, four dierent benchmark problems are proposed, namely, a tapered plate, a quarter of a cylindrical shell, a stiened curved plate, and a curved plate with a degraded material region in stiness, representing a damage. The complexity of these test cases is increased systematically to reveal the advantages and shortcomings of the elements under dierent sensor density deployments. The reference displacement solutions and strain-sensor data used in the benchmark problems are established numerically, utilizing direct finite element analysis. After performing shape-, strain-, and stress-sensing analyses, the reference solutions are compared to the reconstructed solutions of iMIN3, iQS4, and iCS8 models. For plane geometries with sparse sensor configurations, these three elements provide rather close reconstructed-displacement fields with slightly more accurate stress sensing using iCS8 than when using iMIN3/iQS4. It is demonstrated on the curved geometry that the cross-diagonal meshing of a quadrilateral element pattern (e.g., leading to four iMIN3 elements) improves the accuracy of the displacement reconstruction as compared to a single-diagonal meshing strategy (e.g., two iMIN3 elements in a quad-shape element) utilizing iMIN3 element. Nevertheless, regardless of any geometry, sensor density, and meshing strategy, iQS4 has better shape and stress-sensing than iMIN3. As the complexity of the problem is elevated, the predictive capabilities of iCS8 element become obviously superior to that of flat inverse-shell elements (e.g., iMIN3 and iQS4) in terms of both shape sensing and damage detection. Comprehensively speaking, we envisage that the set of scrupulously selected test cases proposed herein can be reliable benchmarks for testing/validating/comparing for the features of newly developed inverse elements

A computational model of peridynamic theory for deflecting behavior of crack propagation with micro-cracks

The critical effect of micro level defects should be examined at macro level to better understand the fracture behaviors of engineering materials. This study investigates the branching and deflecting behavior of a macro (main) crack in presence of multiple number of micro-cracks at the vicinity of the crack tip. For this purpose, a non-local continuum theory, known as Peridynamics (PD), is utilized based on the original set of bond-based PD equations. The main advantage of using PD is its characteristic superiorities on the modelling of dynamical fracture. Various example problems with inclined-linear and/or curvilinear micro-crack clusters are solved through the implementation of different numerical models to better understand the micro-crack toughening mechanisms. After validating the PD implementation with a benchmark case, several combinations of multiple micro-cracks with various locations are considered. To capture complex forms of crack branches, the positions of micro-cracks are designated to follow an encircling and spreading patterns at the vicinity of the main-crack tip. Hence, more internal energy is dissipated through the generation of new crack surfaces such that the main-crack deflects along a more twisting path. It has been observed that depending on the amount of dissipated energy, the propagation speed of main-crack alters. Also, it has been demonstrated that encircling potential crack propagation regions with micro-cracks provides an augmented toughness to the brittle materials. Overall, the efficiency and robustness of the PD theory are revealed for simulating crack propagation in brittle materials

Multi-material topology optimization of structures using peridynamics

This study presents a multi-material topology optimization based on Peridynamics (PD). The conventional topology optimization mainly used a mesh-based numerical method, i.e., Finite Element (FE) method. Moving boundaries, large deformations, and cracks/damages are some limitations of the mesh-based numerical method. In this study, PD as a meshless method is proposed to employ in the topology optimization to remove limitations of the mesh-based topology optimization. The minimization of compliance, i.e., strain energy, is chosen as the objective function subjected to the volume constraint. The design variables are the relative density of the candidate materials defined at particles employing gradient based optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. The proposed approach is an alternative and powerful tool for multiple additive manufacturing in finding multi material optimal topologies of the structures with embedded crack

Parameter identification strategy for online detection of faults in smart structures for energy harvesting and sensing

Abstract In this work, we propose a simple computational method to detect faults in smart piezoelectric structures based on a synchronization strategy. The flexible smart structures are in general described as distributed systems governed by partial differential equations. Numerical discetization is employed to derive a reduced order model such as his dynamic response is simulated solving only ordinary differential equations. Then, the parameter identification strategy is formalized as a dynamic optimization and evolution problem through a further proper set of ordinary differential equations. Lyapunov' theorems are employed to derive an integral type identification algorithm and to ensure the convergence of the procedure. The method is suitable to assess and model nonlinearities in the response of a flexible piezoelectric smart device due to material degradation or local failure. These features are very important to detect faults in the structure and to assess the system reconfiguration properties in real time

A quadrilateral inverse-shell element with drilling degrees of freedom for shape sensing and structural health monitoring

The inverse Finite Element Method (iFEM) is a state-of-the-art methodology originally introduced by Tessler and Spangler for real-time reconstruction of full-field structural displacements in plate and shell structures that are instrumented by strain sensors. This inverse problem is commonly known as shape sensing. In this effort, a new four-node quadrilateral inverse-shell element, iQS4, is developed that expands the library of existing iFEM-based elements. This new element includes hierarchical drilling rotation degrees-of-freedom (DOF) and further extends the practical usefulness of iFEM for shape sensing analysis of large-scale structures. The iFEM/iQS4 formulation is derived from a weighted-least-squares functional that has Mindlin theory as its kinematic framework. Two validation problems, (1) a cantilevered plate under static transverse force near the free tip, and (2) a short cantilever beam under shear loading, are solved and discussed in detail. Following the validation cases, the applicability of the iQS4 element to more complex structures is demonstrated by the analysis of a thin-walled cylinder. For this problem, the effects of noisy strain measurements on the accuracy of the iFEM solution are examined using strain measurements that involve five and ten percent random noise, respectively. Finally, the effect of sensor locations, number of sensors, the discretization of the geometry, and the influence of noise on the strain measurements are assessed with respect to the solution accuracy