Elastic Structural Model Research Articles

Reduction of three-dimensional models of elastic thin-walled structures

Reduction of three-dimensional models of elastic thin-walled structures

Real-Time Aerodynamic Load Estimation for Hypersonics via Strain-Based Inverse Maps

This work develops an efficient real-time inverse formulation for inferring the aerodynamic surface pressures on a hypersonic vehicle from sparse measurements of the structural strain. The approach aims to provide real-time estimates of the aerodynamic loads acting on the vehicle for ground and flight testing, as well as guidance, navigation, and control applications. Specifically, the approach targets hypersonic flight conditions where direct measurement of the surface pressures is challenging due to the harsh aerothermal environment. For problems employing a linear elastic structural model, the inference problem can be posed as a least-squares problem with a linear constraint arising from a finite element discretization of the governing elasticity partial differential equation. Due to the linearity of the problem, an explicit solution is given by the normal equations. Precomputation of the resulting inverse map enables rapid evaluation of the surface pressure and corresponding integrated quantities, such as the force and moment coefficients. The inverse approach additionally allows for uncertainty quantification, providing insights for theoretical recoverability and robustness to sensor noise. Numerical studies demonstrate the estimator performance for reconstructing the surface pressure field, as well as the force and moment coefficients, for the Initial Concept 3.X (IC3X) conceptual hypersonic vehicle.

Time‐Frequency Analysis of Experimental and Analytical Rotor Thrust during a Rotor Speed Change

A study was conducted examining a small-scale, two‐bladed rotor undergoing a change in rotor speed. The data acquired consists of time histories of nonstationary signals; therefore, a Stockwell transform was employed to analyze the data in lieu of traditional Fourier transform-based methods. The analysis included extraction of time‐varying frequency content of the rotor thrust and hub motion, instantaneous rotor speed, damping ratios, and instantaneous phase difference between thrust and hub motion. This work is divided into two parts. First, an analytical study was conducted to understand how rotor transient response, determined using a time‐marching solution, is affected by the inclusion of a simplified elastic support structure model, and is used to demonstrate the utility of the Stockwell transform. The second part of the study compared the results from an analytical model of the NASA Multirotor Test Bed (MTB) undergoing a rotor speed change to wind tunnel data. The current analytical model of the MTB, including an elastic support structure, properly predicted the measured trends in the frequency content of the thrust; however, it underpredicted the amplitude of these unsteady loads.

Experimentally validated numerical prediction of laser welding induced distortions of Al alloy parts for railcar body by inherent strain method combined with thermo-elastic-plastic FE model

A laser welding with wire filler feeding was developed to replace traditional arc welding process for joining aluminium alloy railcar body components. A three-dimensional (3D) thermo-elastic-plastic finite element (FE) model was applied to compute the plastic strains of weld zone in a downsized aluminium alloy plate with butt-joint, T-joint and fillet-joint configurations, respectively, combined with corresponding experimental validations. The achieved plastic strains at the weld zone were then input as inherent strain loadings into elastic structural FE model of fully sized aluminium alloy railcar body components to predict the welding induced distortion with the experimentally measured out-of-plane distortions. The experimentally validated FE model was then further applied for optimizing the inverse pre-deformation of plates to counteract the welding induced deformation, finally to mitigate the welding distortion issues.

Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries.

Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.

Connecting performance evaluation of the Quick-Connector for modular steel construction

This study presents the Quick-Connector, a new self-fastening joint system designed specifically for modular steel construction. By eliminating the need for a dedicated workspace during the connection process, the Quick-Connector minimizes disruptions to finishing work. A comprehensive set of tests, including pull-out, shear, and cyclic tests, was conducted on a full-scale prototype to evaluate its structural performance. The experimental results demonstrate that the Quick-Connector exhibits exceptional connecting performance, meeting the shear and tensile strength requirements for high-tension bolts. The seismic performance of the Quick-Connector was also evaluated through cyclic testing, highlighting its potential as a viable replacement for high-tensile bolts. Furthermore, a push-over analysis was carried out to develop an elastic structural design model specifically for buildings incorporating the Quick-Connector. The analysis results closely aligned with the experimental findings, validating the accuracy of the proposed model. Overall, the Quick-Connector offers a promising alternative to traditional bolted connections in modular construction, with the potential to enhance construction efficiency, quality, and safety.

3D numerical investigation of wave-induced seabed response around a tripod pile foundation with different arrangements

This paper developed an integrated numerical model for the dynamic response of the seabed around tripod turbine foundations under dynamic wave pressure. Three-dimensional (3D) numerical analysis is performed by applying an integrated multiphysics model developed in the finite volume method (FVM) based on the OpenFOAM framework. The present work adopts nonlinear wave model, linear elastic structure model, and anisotropic porous seabed model for wave-structure-seabed interactions. Accuracy of the wave-structure-seabed coupling process was ensured by comparing the numerical model with the numerical and experimental results. This study indicates: (1) the existence of tripods will significantly affect the consolidation results of the surrounding seabed; (2) wave force acting on the tripod structure varies with different arrangements, in which the maximum wave force under the wave crest decreases as the angle between wave and structure increases; and (3) the asymmetry 15° arrangement would significantly increase the maximum liquefaction depth of the seabed.

Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction

AbstractIn this article, a methodology for fine scale modeling of large scale linear elastic structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse scale is modeled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed by solving an oversampling problem with random boundary conditions. Herein, we inform the boundary conditions by a global reduced problem and compare our approach using physically meaningful correlated samples with existing approaches using uncorrelated samples. The local spaces are designed such that the local contribution of each subdomain can be coupled in a conforming way, which also preserves the sparsity pattern of standard finite element assembly procedures. Several numerical experiments show the accuracy and efficiency of the method, as well as its potential to reduce the size of the local spaces and the number of training samples compared to the uncorrelated sampling.

A fidelity equivalence computation method for topology optimization of geometrically nonlinear structures

The application of geometrically nonlinear topology optimization under large deformations in engineering is seriously hindered by its excessive time consumption. To this end, a fidelity equivalent computation method (FECM) with double optimization loops is proposed, in which the topology optimization (TO) model of linear elastic structure is regarded as the low-fidelity TO model of a geometrically nonlinear structure. Then, the geometrically nonlinear TO model is approached in a piecewise manner by a linear TO model using the equivalent factor. Accordingly, the sensitivities of geometrically nonlinear TO are transformed into the sensitivities of linear TO to capture the layouts of the geometrically nonlinear TO model. Moreover, computational accuracy is demonstrated. The validity and feasibility of the proposed FECM are verified through five numerical examples, and the results demonstrate that the FECM can provide sufficient accuracy for solving the TO problem of geometrically nonlinear structures with a relatively small computational cost.

Development of a Stable Implicit Method Without Numerical Dissipation for Nonlinear Structural Dynamic Analysis

This paper develops a self-starting implicit time integration method for nonlinear dynamic analysis. The method is single-step and is based on a non-dissipative second-order accurate approximation scheme. The method employs simple expressions for velocity and acceleration while internal forces are calculated at a specified point. This point results from a weighted combination of the relevant displacements and velocities at the bounds of the time step. In the linear case, the scheme is unconditionally stable, there is no amplitude decay for any time step value and the period elongation is the same as in the Newmark scheme. In nonlinear case, the scheme maintains the same numerical characteristics of dissipation and dispersion of the Newmark scheme while demonstrating a substantial improvement in stability. Summarizing, the presented scheme (i) is a single-step scheme with self-starting attribute; (ii) does not involve additional variables or artificial parameters chosen by the user; (iii) has at least second-order accuracy; (iv) shows to have very wide stability ranges in nonlinear analyses. It also proves that the computational effort per step required by the presented scheme is the same as the effort required in the widely used implicit single-step methods and a substantial reduction in the number of Newton–Raphson iterations in the steps is obtained. For comparison, methods with similar characteristics such as Newmark, generalized-[Formula: see text] and Bathe schemes are tested. Stiff nonlinear problems regarding elastic behavior and finite element structural models are analyzed to compare the considered solution methods.

Analysis of the similarity design and vibration transmission characteristics of typical support structures of an aero-engine

In the vibration test of an entire aero-engine, the magnitude and phase of the unbalanced vector of the internal rotor must be identified based on the vibration signal of the measuring point on the casing. Therefore, in addition to understanding the vibration transmission law between the high- and low-pressure rotors under unbalanced excitation, the vibration transmission law of the support structure must be studied urgently. However, few studies have investigated the vibration transfer characteristics of typical support structures. In this study, the similarity design of typical support structures was first performed, and the structural parameters of the core member squirrel cage were determined using theoretical calculations. Subsequently, the bush and spring elements were used to establish the connection between the inner and outer rings of the bearing to realise the equivalent simulation of the bearing stiffness. Using this method, refined finite element models of elastic and rigid support structures were established, and the accuracy of the model was verified based on low-speed rotating vibration and hammering tests. Furthermore, the unbalanced vibration transmission law of typical support structures was studied, and the vertical vibration transmission law from an aero-engine bearing pedestal to the panel was established with the vibration transmission rate as the quantitative index. Finally, considering the vital role of the squirrel cage, the influence of the local stiffness degradation of the squirrel cage on the unbalanced vibration transmission of the elastic support structure was studied. The research methods and results of this study can provide a basis for aero-engine assembly as well as manufacturing and structural performance evaluation.

Early-stage assessment of structural damage caused by braced excavations: Uncertainty quantification and a probabilistic analysis approach

Current early stage assessment methods for deep excavation induced structural damage have large uncertainty due to modeling idealizations (simplification in analyses) and ignorance (incompleteness of information). This paper implements an elastoplastic two-stage solution of soil-structure-interaction to predict building response to adjacent deep excavations with braced supports. This soil-structure-interaction solution is then used to study the uncertainty in two case studies. A global sensitivity analysis is conducted, which indicates that the prediction of ground movement profiles is the major source of uncertainty in early stage building damage assessment. The uncertainty due to ignorance and idealizations related to structural analysis models also contribute significantly when target buildings are modeled as equivalent beams. However, the use of a 2-dimensional elastic frame structural model, in lieu of an equivalent beam, considerably reduces the assessment uncertainty. Considering the existence of uncertainty, a probabilistic analysis approach is proposed to quantify the uncertainty when predicting potential building damage due to excavation-induced subsidence. A computer program called Uncertainty Quantification in Excavation-Structure Interaction (UQESI) is developed to implement this probabilistic analysis approach.

An FBG Pressure Sensor Based on Spring-Diaphragm Elastic Structure for Ultimate Pressure Detection

We demonstrate a fiber Bragg grating (FBG) pressure sensor based on a spring-diaphragm elastic structure (SDES) for measuring ultimate pressure. The spring-diaphragm elastic structure model can effectively prevent the fiber Bragg grating from being broken under large pressure situations. The geometrical parameters of the sensor are optimally optimized by analyzing the structure of the spring and the diaphragm. By analyzing the results based on the spring-diaphragm elastic structure, the pressure sensor is manufactured and experimentally verified for extreme pressure conditions. For the first time, the fiber Bragg grating pressure sensor was operated at the ultimate pressure. The ultimate pressure experiment demonstrates a stable linear relationship between the fiber Bragg grating central wavelength and external pressure in the range of 0&#x2013;100 MPa, and the sensitivity of the pressure sensor is 79.7 pm/MPa with a linear correlation coefficient of 0.9998. In addition, the relative temperature sensitivity coefficients of the FBGs were obtained as <inline-formula> <tex-math notation="LaTeX">${K}_{P} =5.99 \times 10^{-6}/^{\circ }\text{C}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${K}_{T} =6.265 \times 10^{-6}/^{\circ }\text{C}$ </tex-math></inline-formula> respectively to eliminate the temperature cross-sensitivity effect. The pressure sensor can be used for ultimate pressure detection, especially for deep sea detection, oil exploration, and chemical monitoring.

Level‐wise strain recovery and error estimation for natural element hierarchical plate models

AbstractDiffering from the finite element method, most of mesh‐free methods are restricted to two‐dimensional (2D) problems owing to the difficulty in constructing three‐dimensional (3D) grids. But, for 3D elastic structures, this limitation could be effectively overcome when hierarchical models are employed. In the hierarchical models of elastic structures, only the in‐plane displacement field is needed to be approximated because the thickness‐wise displacement field is assumed by polynomials. In this context, this paper is concerned with the reliable numerical implementation of hierarchical models for plate‐like structures using 2D natural element method (NEM). However, one critical problem in implementing the hierarchical model is to secure the continuity in strain and stress fields. To resolve this problem, this paper presents a level‐wise strain recovery method. In addition, a recovery‐based error estimation is introduced to predict the modeling error and the numerical approximation error. The proposed methods are illustrated and validated through the numerical experiments. It is confirmed that the level‐wise strain recovery successfully and CPU‐time effectively provides the continuous stress resultants and the proposed error estimator accurately predicts the modeling and approximation errors.

Development of a hybrid model based on mesh and meshfree methods and its application to fluid–elastic structure interaction for free surface waves

In this paper, a hybrid scheme, Fluid–Fluid–Elastic Structure (FFES) model was developed in the time domain to address the wave breaking impact on the structure. The model is developed based on the partitioned approach with different governing equations that describe various regions of the model domain. The fluid–fluid model denotes that two different fluid models were used to describe fluid in the actual physical domain. The method is a physics-based approximation to reduce the computational time, i.e. in the far-field inviscid fluid (fully nonlinear potential flow theory model), and near to the structure, viscous fluid (Navier Stokes model) is used. The coupled model then interacts with the elastic structure (based on Euler–Bernoulli beam theory). The system of equations is strongly coupled both in space and time. The Fluid–Fluid coupling uses an implicit predictor–corrector scheme, and the fluid–structure coupling works based on an iterative scheme. This approach makes the method more robust and for future extension. Three different possibilities for introducing the coupling was identified and implemented. The model was validated against results from the analytical solution and literature. The method proposed is a reliable, robust, and efficient alternative for simulating fluid–structure interaction problems.

Natural element approximation of hierarchical models of plate-like elastic structures

Almost all the mesh-free methods are restricted to 2-D problems owing to the difficulty in generating 3-D grids. One effective way to overcome this limitation is to utilize the concept of hierarchical modeling for elastic structures. It was introduced originally for the dimensionally-reduced analysis of 3-D structures, but it can be used for the reverse purpose. By assuming the displacement field in the thickness direction with polynomials, the in-plane displacement could be approximated by 2-D mesh-free method. Inspired this motivation, this paper intends to demonstrate the numerical analysis of plate-like structures by 2-D natural element method (NEM). The polynomial order in the thickness direction is defined by the model level, and a number of hierarchical models are constructed by sequentially increasing the model level. The mid-surface of structure is discretized into a NEM grid and the corresponding in-plane displacement field is approximated according to a locking-free selectively reduced integration technique. The numerical experiments are performed to illustrate and validate the proposed method. Both the central deflection and the stress resultants are investigated with respect to the model level and compared with the full 3-D elasticity. In addition, the modeling error of hierarchical models is examined with respect to the thickness and the model level, and the convergence characteristic to the total number of grid points is compared with FEM.

Formation of mathematical models of stationary dynamics of structures which include thin elastic plates with distributed inertial parameters

This paper is devoted to the problems of modeling stationary oscillatory processes in elastic systems that contain thin-walled plates. The described method allows us to include the mathematical formalization of thin-walled plates in oscillatory models of elastic structures with irregular boundaries of computational areas and heterogeneous boundary conditions. The formation of dynamic models of this kind is based on the use of discretization methods, in particular, finite element methods that allows approximating the initial models with distributed inertial and rigid parameters — discrete ones with concentration of parameters at certain points — nodes of a dynamic system. Obviously, such approximations are accompanied by errors, the estimation of which is extremely difficult to perform under the conditions of the mentioned heterogeneities and irregularities even in the interval variants. In the present work, the construction of elements of bending stationary vibrations of thin-walled plates under monoharmonic effects is proposed. Possessing all the properties of a finite element, the proposed element contains the values of the distributed masses as parameters. In contrast to the use of discretized parameters obtained by using the classical finite element, the proposed method eliminates discretization procedures and thus, eliminates the process of forming mathematical models from additional errors associated with discretization procedures. This element of mathematical modeling of the dynamics of bending is called a harmonic element (HaE). The proposed method is based on the development of dynamic compliance methods, previously used to simulate oscillations of beam systems with distributed parameters. The developed mathematical models of stationary oscillations of thin elastic plates with distributed inertial parameters make it possible to include them in discrete-continuous models containing infinite-dimensional flexural elements (plates and beams), material points, solids and concentrated elasticities. Thus, dynamic models of structures subjected to harmonic effects are represented by a set of harmonic elements (HaE), which allow harmonic matching of heterogeneous elements under different boundary conditions.

Temperature-related study on buckling properties of double-walled carbon nanotubes

In this paper, the influence of finite temperature on the axial buckling of double walled carbon nanotubes (DWCNTs) is investigated based on the non-local Timoshenko beam model. The double walled carbon nanotube with different nonlocal effects is considered as an elastic structure model of mechanics, which is composed of the Van der Waals' force between the two-layers/two walls of carbon nanotubes. Molecular structure mechanics model incorporating thermal temperature is developed to study the relation between Young's modulus and temperature. The temperature dependent Young's modulus is applied to study the mechanical property of double walled carbon nanotubes. It is found that the axial buckling properties of DWCNTs decrease with the increase of the finite temperature at high temperature, however, the axial buckling properties of DWCNTs increase with the increase of the finite temperature at low or room temperature. Moreover, it is noted that the continuous temperature has litter effect on the axial buckling property of DWCNTs at the low temperature. However, the influence of continuous temperature on the mechanical properties of DWCNTs can not be neglected at the high temperature.

Numerical investigation on dynamic ultimate strength of stiffened panels considering real loading scenarios

ABSTRACTIn the last 10 years, the importance of whipping on the extreme hull girder loads has received much attention from designers and classification societies. The most common practice to evaluate the ultimate strength of a relatively soft floating structure is to compare the maximum dynamic vertical bending moment after a slamming event with the quasi-static hull girder capacity. Some aspects regarding the current procedure remain unclear, like the capability of the current hydro-elastic methods to accurately predict the extreme dynamic response on the basis of a linear elastic structural model. Moreover, the whipping-induced stresses have a higher frequency than the ordinary wave-induced stresses; hence, the dynamic effects may provide additional strength reserves for the structure and should be investigated. Therefore, the aim of this paper is to investigate the dynamic ultimate strength of stiffened panels considering real loading scenarios, associated with wave loads and whipping response.

Characterization of a controllable stiffness foil bearing with shape memory alloy springs

Abstract This paper develops a shape memory alloy gas foil bearing (SMA-GFB), in which the stiffness of elastic structure and the clearance between the rotor and top foil are adjusted by the temperature of SMA springs which is controlled by electric heating and a designed cooling method. A numerical model of elastic structure composed by a series of SMA springs is conducted, and the experimental results verify that the active elastic structure can improve SMA-GFB performance. Furthermore, the static and dynamic characteristics of SMA-GFBs are predicted. The load capacity and stability of two different designs of SMA-GFB are explored based on the circumferential distribution of SMA springs. These data expand the path for the active application of SMA in gas bearings.