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

An enhanced inverse finite element method for displacement and stress monitoring of multilayered composite and sandwich structures

The inverse finite element method (iFEM) is an innovative framework for dynamic tracking of full-field structural displacements and stresses in structures that are instrumented with a network of strain sensors. In this study, an improved iFEM formulation is proposed for displacement and stress monitoring of laminated composite and sandwich plates and shells. The formulation includes the kinematics of Refined Zigzag Theory (RZT) as its baseline. The present iFEM methodology minimizes a weighted-least-squares functional that uses the complete set of strain measures of RZT. The main advantage of the current formulation is that highly accurate through-the-thickness distributions of displacements, strains, and stresses are attainable using an element based on simple C0-continuous displacement interpolation functions. Moreover, a relatively small number of strain gauges is required. A three-node inverse-shell element, named i3-RZT, is developed. Two example problems are examined in detail: (1) a simply supported rectangular laminated composite plate and (2) a wedge structure with a hole near one of the clamped ends. The numerical results demonstrate the superior capability and potential applicability of the i3-RZT/iFEM methodology for performing accurate shape and stress sensing of complex composite structures

Dynamic fracture analysis of functionally graded materials using ordinary state-based peridynamics

Functionally graded materials are regarded as a special kind of composites capable of eliminating material interfaces and the delamination problems. Stress discontinuity can be avoided owing to smooth composition of the functionally graded ingredients. In this study, a recently emerged effective non-local continuum theory for solving fracture problems in solids and structures, peridynamics, is employed to simulate dynamic wave propagation as well as crack propagation in functionally graded materials. Specifically, the ordinary state-based formulation is adopted. The ordinary state-based formulation is slightly modified for the modelling of functionally graded materials. The averaging technique is employed to determine peridynamic parameters associated with the material properties. Firstly, a benchmark problem is considered to validate the present implementation of ordinary state-based peridynamics for brittle fracture of homogeneous materials. Then, the wave propagation in the functionally graded materials under impact loading is simulated. Finally, dynamic crack propagation in the functionally graded materials is studied. The evaluated crack paths and the displacement waves are compared with reference works including numerical and experimental results. Good agreement between the reference and present results is achieved. It is shown that a simple modification of ordinary state-based formulation has led to simulate dynamic fracture of functionally graded materials

Topology optimization of cracked structures using peridynamics

Finite element method (FEM) is commonly used with topology optimization algorithms to determine optimum topology of load bearing structures. However, it may possess various difficulties and limitations for handling the problems with moving boundaries, large deformations, and cracks/damages. To remove limitations of the mesh-based topology optimization, this study presents a robust and accurate approach based on the innovative coupling of Peridynamics (PD) (a meshless method) and topology optimization (TO), abbreviated as PD-TO. The minimization of compliance, i.e., strain energy, is chosen as the objective function subjected to the volume constraint. The design variable is the relative density defined at each particle employing bi-directional evolutionary optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. To present the capability, efficiency and accuracy of the PD-TO approach, various challenging optimization problems with and without defects (cracks) are solved under different boundary conditions. The results are extensively compared and validated with those obtained by element free Galerkin method and FEM. The main advantage of the PD-TO methodology is its ability to handle topology optimization problems of cracked structures without requiring complex treatments for mesh connectivity. Hence, it can be an alternative and powerful tool in finding optimal topologies that can circumvent crack propagation and growth in two and three dimensional structures

Structural health monitoring of an offshore wind turbine tower using iFEM methodology

With the increasing popularity of wind energy, offshore wind turbines (OWTs) are currently experiencing rapid development. The tower is one of the most significant components of the OWT. However, the tower will not only stand its own weight and weight of the top structure, but also be surrounded by harsh wave and wind loading conditions. Therefore, it is necessary to apply a structural health monitoring (SHM) system to monitor the health condition of the OWT towers in real-time. In this study, inverse Finite Element Method (iFEM) is applied to monitor the tower of an OWT under both static and dynamic loading conditions. The total displacements and von Mises stresses obtained from iFEM analysis are compared against reference results and optimum sensor locations are determined

Structural health monitoring of an offshore wind turbine tower using iFEM methodology

With the increasing popularity of wind energy, offshore wind turbines (OWTs) are currently experiencing rapid development. The tower is one of the most significant components of the OWT. However, the tower will not only stand its own weight and weight of the top structure, but also be surrounded by harsh wave and wind loading conditions. Therefore, it is necessary to apply a structural health monitoring (SHM) system to monitor the health condition of the OWT towers in real-time. In this study, inverse Finite Element Method (iFEM) is applied to monitor the tower of an OWT under both static and dynamic loading conditions. The total displacements and von Mises stresses obtained from iFEM analysis are compared against reference results and optimum sensor locations are determined