Isogeometric mindlin-reissner inverse-shell element formulation for complex stiffened shell structures

Structural health monitoring (SHM) is a technology that is used to improve the safety, stability, and availability of large engineering structures. One important aspect of SHM is the ability to perform real-time reconstruction of the full-field structural displacements, also known as shape sensing. The inverse Finite Element Method (iFEM) is a technique that has been used for three-dimensional shape sensing of structures using strain data. On the other hand, Isogeometric Analysis (IGA) is a method that utilizes smooth spaces of functions, such as non-uniform rational B-splines, to solve structural problems and has gained significant attention in recent times. In this study, the authors propose a new method for shape sensing of complex stiffened shell structures by combining IGA with the iFEM method. The goal of this research is to accurately reconstruct the complex geometry of the structure without the need for a fine numerical discretization or mesh. To achieve this, the authors have developed an isogeometric Mindlin-Reissner inverse-shell element (IgaiMin) to implement the coupling between IGA and iFEM. The proposed method is validated by solving problems involving simple plates, tee junctions, and partly clamped stiffened panels representing ship structures

Two-node curved inverse finite element formulations based on exact strain-displacement solution

The inverse finite element method (iFEM) is an efficient algorithm developed for real-time monitoring of structures equipped by a network of strain sensors. The inverse element for modeling curved beams was previously developed using an approximate solution based on independently interpolated displacement components. In this study, a new formulation is proposed by the development of a least-squares variational principle using the kinematic framework of the curved beam theory. The library of existing iFEM-based elements is expanded by introducing three different inverse curved elements named iCB3, iCB4 and iCB5 respectively. This new formulation has been developed considering the exact solution of the curved beam theory that corresponds to the membrane-bending coupling and the explicit statement of the rigid-body motions. The three inverse elements, which require three, four and five measurement points respectively, extend the practical utility of iFEM for shape sensing analysis of curved structures according to the minimum available quantity of strain sensors. The effectiveness and higher accuracy of the iCB/iFEM methodology compared to other solutions present in literature are demonstrated considering numerical studies on curved beams under static transverse force and distributed loading conditions. For these problems, the effect of strain measurements error, number of sensors and discretization refinement on the solution accuracy is evaluated

Inverse Finite Element Method for Reconstruction of Deformation in the Gantry Structure of Heavy-Duty Machine Tool Using FBG Sensors

The deformation of the gantry structure in heavy-duty machine tools is an important factor that affects machining accuracy. In order to realize real-time monitoring of the deformation of the gantry structure, which is statically indeterminate and complex in shape, the reconstruction algorithm based on inverse Finite Element Method (iFEM) is proposed and fiber Bragg grating (FBG) sensors are used to measure strain data. The elements of the gantry structure are divided and the displacement functions of each element are determined. The shape function is obtained by substituting degree of freedoms (DOF) of element nodes into displacement functions. Through a differential method, the relation between strain and DOF of element nodes is established by the strain matrices. Subsequently, the DOF of element nodes are obtained by minimizing an error functional defined as the least-squares error between the analytic strain data and the corresponding experimental strains. Considering coordinate transformation and problem-specific displacement boundary conditions, the total deformation of the gantry structure is obtained. Following this, the experiment was carried out. The deformation simulated by ANSYS was used to replace the experimentally measured deformation and then compared with the deformation reconstructed by iFEM under the same loading condition. The accuracy of iFEM for reconstructing deformation of the gantry structure in heavy-duty machine tools is verified. It provides a new view for improving the machining precision of heavy-duty machine tools

Inverse Finite Element Method for Reconstruction of Deformation in the Gantry Structure of Heavy-Duty Machine Tool Using FBG Sensors

The deformation of the gantry structure in heavy-duty machine tools is an important factor that affects machining accuracy. In order to realize real-time monitoring of the deformation of the gantry structure, which is statically indeterminate and complex in shape, the reconstruction algorithm based on inverse Finite Element Method (iFEM) is proposed and fiber Bragg grating (FBG) sensors are used to measure strain data. The elements of the gantry structure are divided and the displacement functions of each element are determined. The shape function is obtained by substituting degree of freedoms (DOF) of element nodes into displacement functions. Through a differential method, the relation between strain and DOF of element nodes is established by the strain matrices. Subsequently, the DOF of element nodes are obtained by minimizing an error functional defined as the least-squares error between the analytic strain data and the corresponding experimental strains. Considering coordinate transformation and problem-specific displacement boundary conditions, the total deformation of the gantry structure is obtained. Following this, the experiment was carried out. The deformation simulated by ANSYS was used to replace the experimentally measured deformation and then compared with the deformation reconstructed by iFEM under the same loading condition. The accuracy of iFEM for reconstructing deformation of the gantry structure in heavy-duty machine tools is verified. It provides a new view for improving the machining precision of heavy-duty machine tools