Structural deformation reconstruction by the Penrose–Moore pseudo-inverse and singular value decomposition–estimated equivalent force

For structural health monitoring, estimating the external load is a typical ill-posed problem but significant. Because with the external force and the structural finite element model, any required response can be calculated, which is advantageous for further structural health monitoring works. This article first defines an underdetermined equation using a limited number of in-field measurements and the finite element model–calculated influence line matrix, and it proposes a load estimation method using the Penrose–Moore pseudo-inverse (generalized inverse). The objective of the proposed method is to obtain the equivalent nodal force vector with minimum length among all possible force vectors satisfying the deformation constraints. The estimated force is an equivalent nodal force, since it only satisfies limited deformation constraints. With the estimated nodal force, full structure static response can be easily calculated by multiplying the influence line matrix and the equivalent force vector. Besides, the truncated singular value decomposition is used to process the finite element model–calculated influence line matrix to avoid the over-fitting effect due to the measurement noise. The singular values of singular value decomposition represent the significance of the structural deformation modes, and the decreasing rate of the singular values is a good complexity indicator for a structure. The proposed frame can involve any types of static measurements, and it can realize real-time computation because it merely involves the matrix multiplying calculation. Finally, the sensitivity analysis is conducted by numerical simulation, and a large-scale model-based experiment has demonstrated that the algorithm is appropriate for in-field applications.

Hyperelastic membrane modelling based on data-driven constitutive relations

We present data-driven modelling of membrane deformation by a hyperelastic nodal force method. We assume that constitutive relations are characterized by tabulated experimental data instead of the conventional phenomenological approach. As experimental data we use synthetic data from the bulge test simulation for neo-Hookean and Gent materials. The numerical study of descriptive and predictive capabilities of our approach demonstrates very good results of the data-driven modelling provided that the input tabulated data are expanded to a wider region of strain characteristics. Two methods for such expansion are suggested and numerically studied. Different loadings of hyperelastic membranes are successfully recovered by our approach.

Structural response reconstruction using inclinometer and velocimeter

<p>This paper proposes a structural dynamic response reconstruction algorithm using inclinometer and velocimeter, combining in-situ measured data with finite element model. Using a small number of inclination and velocity data, the dynamic deflection, rotation, and strain at any position of a structure can be estimated. Firstly, static structural deformation estimation method is introduced as the base. The key content is to solve an underdetermined static equation using partial least square regression and calculate equivalent nodal force. By rewriting dynamic balance equation into state space, an equivalent static balance equation is obtained. Use partial least square regression to solve this equation and compute time histogram of equivalent nodal force, in which dynamic distortion exists. Accordingly, a frequency response-based time interval correction method is proposed to correct the dynamic distortion and is validated to be effective. Finally, numerical simulation is adopted to validate accuracy and robustness of the algorithm through changing parameters including sampling time interval, input frequency components, model parameters and introducing measurement noise. All results have demonstrated that the algorithm is of good adaptability to various changes and maintains high accuracy.</p>

A Hybrid Interpolation Method for Geometric Nonlinear Spatial Beam Elements with Explicit Nodal Force

Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.

A High Precision and Convenient Method to Analyze the Mechanics of Scissor Lift Platform under the Action of Combined Loads

Scissor lift platform had lots of kinematic pairs and the mechanics relations between them were complex. So mechanics analysis became the focus by researchers. The mechanical model of scissor lift platform under the action of combined loads was built in the paper. The calculation formula of nodal force of scissor transmission unit was given used the transfer matrix method. The calculation formulas of drive units were given on the virtual work principle. Also the calculation method of nodal forces of drive units was given. How the different distributions of drive unit influence on the nodal force was analyzed. The drive units’s position optimization method was given in this paper. In order to verify the reliability of this calculation method, an calculation example of typical structure was given. The calculation results given by the method in this paper was identical with the result given by finite element method. The conclusions obtained could serve as theoretical guidance and reference for mechanical analysis and optimal design of scissor transmission mechanism.