Nodal Displacements Research Articles

Automated Pipeline for the Analysis of a Scale‐reduced Steel Cable Net

AbstractThis paper proposes a digitally twinned experimental analysis of a scale‐reduced laboratory‐sized steel cable net subjected to vertical loading. The test is aimed at establishing automated pipelines of information and analysis between the measurements (displacements of nodes) and the numerical model of the cable net, which are seamlessly interconnected through a BIM model. These automated pipelines erect the frame of the development of a digital twin of the cable net with structural analysis purposes. For the sake of measurements, a terrestrial laser scanner is used. Displacements of the nodes are extracted using computational geometry tools. For the sake of analysis, a data‐based numerical model is proposed to obtain the tensile state of the cables. Precisely understanding the force distribution along nets is a challenge at design, construction and operation stages. This research belongs to a vaster project related to the development of automated pipelines of information for European infrastructure in the form of digital twins. The outcome of this laboratory test results is of great use when developing similar automated pipelines of information in real sites including cable nets in roofs.

Three dimensional modeling and numerical analysis of hydrogen effects on the thermomechanical response of Nickel–Titanium orthodontic applications

This paper deals with effects of the hydrogen presence on the thermo-mechanical behavior of NiTi shape memory alloys (SMAs), widely considered for manufacturing orthodontic archwires. A three dimensional phenomenological model is formulated, based on thermodynamics of irreversible processes. It takes into account the experimentally observed effects on the main physical mechanisms (martensitic transformation and reorientation of martensite). The assumption of an additive decomposition between a reversible lattice and a trapped hydrogen concentrations is adopted. The complete problem including chemical, thermal and mechanical balanced equations and their weak form are solved by the finite element method. A 3D hexahedral continuum finite element with five degrees of freedom per node (displacements, temperature and total hydrogen concentration) is developed. Its implementation is carried out in the Abaqus finite element software. Numerical results are presented and compared to experimental ones which show the significant effects of the hydrogen presence in NiTi SMA.

Gaussian Stochastic Process Modeling of Blend Repaired Airfoil Modal Response Using Reduced Basis Mode Shape Approach

Abstract A machine learning (ML) approach is developed to predict the effect of blend repairs on airfoil frequency, modal assurance criterion (MAC), and modal displacement vectors. The method is demonstrated on a transonic research rig compressor rotor airfoil. A parametric definition of blend geometry is developed and shown to be capable of encompassing a large range of blend geometry. This blend repair geometry is used to modify the airfoil surface definition and a mesh morphing process transforms the nominal finite element model (FEM) to the repaired configuration. A multilevel full factorial sampling of the blend repair design space provides training data to a Gaussian stochastic process (GSP) regressor. The frequency and MAC results create a vector of training data for GSP calibration, but the airfoil mode shapes require further mathematical manipulation to avoid creating GSP models for each nodal displacement. This paper develops a method to significantly reduce blended airfoil mode shape emulation cost by transforming the mode shape training data into a reduced basis space using principal component analysis (PCA). The coefficients of this reduced basis are used to train a GSP that can then predict the values for new blended airfoils. The emulated coefficients are used with the reduced basis vectors in a reconstruction of blended airfoil mode shape. Validation data is computed at a full-factorial design that maximizes the distance from training points. It is found that large variations in modal properties from large blend repairs can be accurately emulated with a reasonable number of training points. The reduced basis approach of mode shape variation is shown to more accurately predict MAC variation when compared to direct MAC emulation. The added benefit of having the full modal displacement field also allows determination of other influences such as tip-timing limits and modal force values.

An inverse analysis method to identify maximum overfire temperature based on an improved ant colony algorithm

There are many causes of building fire incidents that can manifest in many forms. Overfire temperature is one of the most important factors affecting structural residual deformation, and it is the basic parameter for postfire structural safety evaluations. To study the overfire temperature and the temperature field distribution of a structure under fire, an overfire temperature inversion method based on an improved ant colony algorithm has been proposed, where the entire structure is discretized into multiple zones and the zonal maximum overfire temperature is assumed to be the load action. The finite element software ANSYS is used for developing a numerical model of the structure, and a positive analysis is applied to the mechanical response of the structure under fire. As a result, the residual displacements of each zone are obtained, the minimum differences between the numerical and measured displacements are considered as the target function, the overfire temperature is assumed to be the design variable, the improved ant colony algorithm is utilised to inversely analyse the structure at the overfire temperature, the highest overfire temperature is determined, and the temperature field distribution of the structure under fire is obtained. Furthermore, a scale model fire test of the space grid structure is performed, and the fire temperature and node displacements are recorded. The inverse method is applied to the fire test model to verify its feasibility and effectiveness. The results suggest that the ant colony algorithm has good applicability to structure overfire temperature inverse analysis.

Effective linear wave motion in periodic origami structures

We establish a dynamic homogenization framework catering for the linear elastic wave motion in periodic origami structures. The latter are modeled via “bar-and-hinge” paradigm where: (i) the folding of the structure and the bending of individual panels are modeled via elastic hinges, and (ii) the in-plane deformation of each panel is modeled with elastic bars. Using the so-formulated discrete model of an origami structure, we pursue finite wavenumber-finite frequency (FW-FF) homogenization of the wave motion in a spectral neighborhood of simple, repeated, and nearby eigenfrequencies at an arbitrary wavenumber within the first Brillouin zone. The lynchpin of the proposed approach is the “projection” of the nodal displacements over each unit cell onto a suitable Bloch eigenvector, evaluated at the “center” of the spectral region of interest. For completeness, we make an account for: (i) the source term acting at the nodes of a discrete structure, and (ii) periodic Dirichlet boundary conditions. We obtain the leading-order (system of) effective equation(s) synthesizing the wave motion in a selected spectral neighborhood, and we describe asymptotically the corresponding dispersion relationship. We illustrate the proposed framework by comparing numerically the Bloch dispersion relationship to its asymptotic approximation for (a) a 2D-periodic Miura-ori structure, and (b) a 1D-periodic Miura tube. The dispersion analysis is complemented by evaluating the effective wave motion (in terms of both “macroscopic” and “microscopic” essentials) in a 2D-periodic Miura-ori structure due to spatially-localized source term acting either inside a band gap or within a passband.

Using automatically generated submodels in vehicle body crash optimization

In order to perform optimizations with vehicle models efficiently, the resource requirements for a simulation must be reduced. In this article, approaches for the physical reduction of the vehicle model are presented, which automatically removes components or elements from the model. For the reduction, evaluation functions considering the crash behaviour of the model are used, as well as geometric methods that ensure its viability. Suitable boundary conditions, such as an equivalent mass or displacements of individual nodes, are applied to the reduced model to recover the kinematics. Finally, the practical application of the methodology is presented by two optimizations.

Model test study on static performance of rib-patterned small rise-span ratio suspend-dome structure

To investigate the distribution characteristics of prestressing force and static characteristics of the rib-patterned small rise-span ratio suspend-dome structure, a 1:20 scaled model of the Lanzhou Olympic Gymnasium roof structure was established. During to the small-scale ratio model with dense nodes, according to the principle of constant structural stiffness, a multi-node synchronous loading device was designed. The construction tensile loading test and multi-stage static loading test were carried out. The axial force of rods, vertical displacement of nodes, and radial displacement of supports for the model with initial geometric imperfection under 11 load cases were tested. Test results were used to validate and then refine the numerical simulation using ABAQUS. The study shows that a multi-node synchronous loading device dramatically improved the loading efficiency and satisfied the accuracy requirement of the test. The test results were in good agreement with the simulated results, which verified the correctness of the finite element modelling method, the accuracy of the test method, and the rationality of the measuring point arrangement. The small rise-span ratio suspend-dome structure with a rib-patterned has good elasticity at a low load level. The full-span arrangement of the live load is the most unfavorable load case of the structure. The outer loop cable bearing capacity exhibited a higher proportion. The third ring rod was found to sustain the highest load, the outer ring rod is more sensitive to load, and the fourth circle node was found to have the largest vertical displacement in the model. The change of support displacement in practical engineering should not be neglected.

Effects of interdiffusion on shear response of semi-coherent {111} interfaces in Ni/Cu

Intermixing of chemical species as a result of interdiffusion during the manufacturing of metallic nanolaminates leads to diffuse interface structures which have distinct properties compared to corresponding atomically sharp interfaces. The effect of interdiffusion-induced changes to the interface structure on interface shear strength is complex due to the presence of solute atoms and a reduced misfit dislocation density. The shear responses of {111} Cu/Ni nanolaminate interfaces with varying levels of interdiffusion are studied using atomistic methods to elucidate the effect of interface structure changes on shear deformation mechanisms. Models with diffuse interfaces exhibit improved interface shear strength relative to the atomically sharp case; however, shear strength does not increase monotonically with solute concentration. The distribution of maximum changes in energy per misfit node and non-uniform misfit node displacements, filtered using microrotation vector analysis, suggest heterogeneous interface resistance to sliding. No strong correlation is found between solute concentration near misfit node centroids and misfit node displacements, indicating the importance of the longer-range misfit dislocation structure. Increased activation of misfit dislocation glide is associated with larger solute concentrations as a result of increased misfit node displacements. Analysis of change in energy during the shear deformation process, however, reveals that interface sliding is dominated by the misfit node behavior. These findings highlight the importance of modeling realistic diffuse interface structures and emphasize the competing effects of solute concentration and interface misfit dislocation density.

An Optimized Model for the Approximate Iterative Adjustment of the "FAST" Active Reflector

This paper analyzes the relevant data and finds that the angle formed by the upper endpoint, the lower endpoint, and the main cable node of 2216 groups of actuators is between 179.95° and 180°. Therefore, it is considered that the main cable nodes move mainly in the radial direction, and only a small amount of tangential displacement occurs. Then, mathematical models are established for the radial and tangential displacements, and after several iterations, the coordinates before and after the displacement of the main cable node are obtained. Since the adjustment factors of the reflective panel need to be considered in combination, the reflective panel is easy to adjust. The shortest total telescopic distance of the actuator is the optimization goal, and the optimization model is established with the adjustment factors and other constraints as the constraints.

Design and validation of a finite element model of the aponeurotic and free Achilles tendon.

The Achilles tendon (AT) is a common injury site. Ruptures are usually located in the free tendon but may cross the myotendinous junction into the aponeurotic region. Considering the possibility of aponeurotic region involvement in AT ruptures, a novel three dimensional (3D) finite element (FE) model that includes both the aponeurotic and free AT regions and features subtendon twisting and sliding was developed. It was hypothesized that the model would be able to predict in vivo data collected from the literature, thus being considered valid, and that model outputs would be most sensitive to subtendon twist configurations. The 3D model was constructed using magnetic resonance images. The model was divided into soleus and gastrocnemius subtendons. In addition to a frictionless contact condition, the interaction between subtendons was modeled using two contact formulations: sliding with anisotropic friction and no sliding. Loads were applied on the tendon's most proximal cross-section and anterior surface, with magnitudes estimated from in vivo studies. Model outputs were compared with experimental data regarding 3D deformation, transverse plane rotation, and nodal displacements in the free tendon. The FE model adequately simulated the free tendon behavior regarding longitudinal strain, cross-section area variation, transverse plane rotation, and sagittal nodal displacements, provided that subtendon sliding was allowed. The frictionless model exhibited noticeable medial transverse sliding of the soleus subtendon, which was present to a much lesser degree in the anisotropic friction model. Model outputs were most sensitive to variations in subtendon twist and dispersion of the collagen fiber orientations. Clinical Significance: This Achilles tendon finite element model, validated using in vivo experimental data, may be used to study its mechanical behavior, injury mechanisms, and rupture risk factors.

Finite element solution of vibrations and buckling of laminated thin plates in hygro-thermal environment based on strain gradient theory

The paper aims to develop a finite element methodology to deal with vibrations and buckling of laminated thin plates subjected to thermal and hygroscopic effects, once a second-order strain gradient theory is included to overcome the limitations of conventional elasticity and to capture nonlocal phenomena. The numerical scheme takes advantage of Hermite approximation for both membrane and bending primary variables, since the strain gradient introduces higher-order derivatives of the nodal displacements. Its versatility is proven by dealing with general lamination schemes and arbitrary boundary conditions. The analyzed configurations cannot be solved analytically.

Member importance prediction and failure response analysis for cable network antennas

Cable network antennas are likely to experience damage from the extreme space environment. This will deteriorate the antennas’ performance and even lead to the scrapping of antennas. To date, effective means for on-orbit maintenance of cable network antennas are lacking. Therefore, it is necessary to investigate the influence of each member failure on the antenna and find the most important ones before launching. But the method of exhaustion to analyze each member failure response is inefficient. Hence, we propose an importance prediction method for finding the key members of the antenna based on the sensitivity analysis. The sensitivity analyses with respect to the failure member are carried out, in which the condition of cable slack caused by member failure is considered. The node displacement sensitivity is used to predict the member importance. After that, based on the vector form intrinsic finite element method, a response analysis method for the incomplete antenna after member failure is proposed. The proposed method can accurately capture the transient response of the antenna and effectively avoid the non-convergence problem caused by slack cables. A numerical example is provided, and the most important members are predicted, which should be given special concern in the design stage.

Mechanical properties of topological metamaterials

Recent advances in physics and engineering have led to the discovery of behavioral correlations between thermal, electromagnetic, optical, quantum and classical mechanical metamaterial systems. Of particular interest for the development of novel metamaterial properties is topological polarization, a new mapping established between quantum mechanical topological insulators and mechanical systems. Although recent research has shown many properties of polarized regions in metamaterials, the relationship between the topological effects, force concentration along domain boundaries, and mechanical properties of polarized lattices has found little attention. Further, current findings are also limited to linear continuous boundary regions. Here, we show how the hexagonal Kagome lattice and square lattice in their polarized state can concentrate axial forces along non-linear boundary regions and how the resulting mechanical properties depend on both the direction of the external loading and the magnitude of the nodal displacements used to polarize the given lattices. The results show that the mechanical properties of polarized lattices are primarily informed by the switch from a stretch-dominated to a bending-dominated state during polarization, but also by the increasing force concentration in the domain boundaries. These findings enable the design of complex topological lattices with predetermined concentration behavior while also accounting for changes in the overall mechanical properties.

Formulation of the Green’s functions stiffness method for Euler–Bernoulli beams on elastic Winkler foundation with semi-rigid connections

The Green’s Functions Stiffness Method (GFSM) is a method to compute the analytic closed-form response (reactions, displacements, and internal forces fields) of structures. It merges the strengths of the stiffness method (SM) (an exact relation between forces and displacements at the ends of elements) with those of Green’s functions (computation of closed-form analytic structural response due to any arbitrary load). Its formulation is based on the decomposition of the structural response into homogeneous and fixed parts. The former depends on the degrees of freedom (joints displacements and rotations) and yields the stiffness matrix, while the latter depends on the external loads and is related to the fixed end forces vector. The element response is computed directly from the nodal displacements. First, the displacement fields are computed, and from their derivatives, the internal forces fields are obtained. This paper presents the formulation of the GFSM for Euler–Bernoulli beams on elastic Winkler foundation with semi-rigid connections and, as a particular case, for Euler–Bernoulli beams with semi-rigid connections. Additionally, two examples, and conclusions are presented.

On the role of proppants and geomechanics on flowback behavior in complex fracture networks

Flowback analysis is often used for the post-fracturing characterization of unconventional wells to estimate key reservoir and fracture parameters. However, conventional flowback analysis relies solely on the fluid flow analysis, the potential impact of proppant or geomechanics on flowback behavior is seldom discussed. To fill this gap, an integrated numerical model is proposed here to simulate fracture propagation, well shut-in and finally flow back from fracture network. To simulate the fracture propagation with branches, a cohesive zone model with node displacement is adopted. During fracture closure process, proppant stress is integrated to consider the presence of proppants and non-linear fracture permeability evolution is also considered to represent the transition from fracture flow to Darcy's flow.Simulation results show that the presence of proppants and geomechanics may significantly impact the fracture closure mode and flowback behavior in fracture networks. When proppants are placed in the fracture, an infection point can be identified in the bottomhole pressure (BHP) response. After one day flowback, BHP with proppants is nearly 65% larger than that without proppants. Notably, fracture complexity can also be identified during flowback. As more proppants placed deeply into the fracture network, corresponding BHP would decline at a lower rate with later appearance of the inflection point. Besides, the formation properties near wellbore also affect the flowback behavior. As the permeability in the stimulated zone improves, BHP declines much milder after the inflection point. Finally, larger flowback rate can accelerate the fracture closure and enhance the overall BHP decline rate no matter when the inflection point is. Since most flowback models rely solely on fluid flow component, this study provides a new insight on flowback behavior which incorporate interactions of fluid flow, geomechanics and the presence of proppants.

DYNAMIC BEHAVIOR OF A RC COLUMN UNDER AXIAL-LATERAL IMPACT

The analysis of the collapses of buildings and structures that have occurred in recent decades, as well as the results of experimental studies, shows that a sudden failure of a column of the load-bearing system of a building leads to dynamic effect on structures adjacent to the site of initial local destruction. In this case, the columns adjacent to the site of the initial local destruction can be subjected to the simultaneous action of the axial shock loading and the lateral displacement of the support nodes. In this regard, the subject of the paper is the dynamic behavior of a reinforced concrete column under axial-lateral impact. The paper proposes an analytical solution to the differential equation of the axial-lateral buckling of a reinforced concrete column under accidental impact caused by a sudden structural transformation of the load-bearing system. Nonlinear behavior of material and energy dissipation due to damping have been considered. As a criterion for the bearing capacity assessment, the achievement of zero resistance is accepted, i.e., the ability of cross-section to resist the increment of forces along the height of the column. The results of numerical modeling are compared with the experimental data for lateral displacement obtained by the authors for the model of a two-story reinforced concrete frame with slender columns. The obtained analytical solution allows approximate evaluation the progressive collapse behavior of eccentrically compressed reinforced concrete columns.

A unified newton barrier method for multibody dynamics

We present a simulation framework for multibody dynamics via a universal variational integration. Our method naturally supports mixed rigid-deformables and mixed codimensional geometries, while providing guaranteed numerical convergence and accurate resolution of contact, friction, and a wide range of articulation constraints. We unify (1) the treatment of simulation degrees of freedom for rigid and soft bodies by formulating them both in terms of Lagrangian nodal displacements, (2) the handling of general linear equality joint constraints through an efficient change-of-variable strategy, (3) the enforcement of nonlinear articulation constraints based on novel distance potential energies, (4) the resolution of frictional contact between mixed dimensions and bodies with a variational Incremental Potential Contact formulation, and (5) the modeling of generalized restitution through semi-implicit Rayleigh damping. We conduct extensive unit tests and benchmark studies to demonstrate the efficacy of our method.

2D Numerical Simulation of Auxetic Metamaterials Based on Force and Deformation Consistency

This work showcases a novel phenomenological method to create predictive simulations of metallic lattice structures. The samples were manufactured via laser powder bed fusion (LPBF). Simulating LPBF-manufactured metamaterials accurately presents a challenge. The printed geometry is different from the CAD geometry the lattice is based on. The reasons are intrinsic limitations of the printing process, which cause defects such as pores or rough surfaces. These differences result in material behavior that depends on the surface/volume ratio. To create predictive simulations, this work introduces an approach to setup a calibrated simulation based on a combination of experimental force data and local displacements obtained via global Digital Image Correlation (DIC). The displacement fields are measured via Finite Element based DIC and yield the true local deformation of the structure. By exploiting symmetries of the geometry, a simplified parametrized simulation model is created. The simulation is calibrated via Response Surface Methodology based on nodal displacements from FE-DIC combined with the experimental force/displacement data. This method is used to create a simulation of an anti-tetrachiral, auxetic structure. The transferability and accuracy are discussed, as well as the possible extension into 3D space.

Analysis of wind-induced responses of landing assembled Chinese solar greenhouses

The wind-induced responses of a landing assembled Chinese solar greenhouse (CSG) were investigated by considering fluctuating wind speeds. Fluctuating wind speeds were simulated using the harmony superposition method. The dynamic properties of the CSG were extracted using modal analysis. The displacement and bending stress of the CSG under mean and instantaneous wind loads were compared. The results showed that both the displacement and bending stress under the south wind (0° direction) were lower than those under the north wind (180° direction). When the wind direction was 0°, the maximum displacement and bending stress under instantaneous wind loads were 1.926 and 1.673 times those under mean wind loads, respectively. When the wind direction was 180°, the maximum displacement and bending stress under instantaneous wind loads were 2.054 and 2.003 times those under mean wind loads, respectively. To estimate the nodal displacement wind vibration coefficients and quantify the amplification effects of instantaneous wind loads, the effects of the structural damping ratios, sectional dimensions, and simulated wind speed samples on the wind-induced responses of the CSG were investigated. Finally, a global nodal displacement wind vibration coefficient of 2.0 is recommended for the case study. These results can provide a reference for the wind-resistance design of landing assembled CSG. • Fluctuating wind speeds were simulated using the harmony superposition method. • The wind-induced responses of a landing assembled CSG were investigated. • The dynamic properties of the CSG were extracted using modal analysis. • The nodal displacement wind vibration coefficients were obtained.

An extended fictitious node method for surface effect correction of bond-based peridynamics

The surface effect of peridynamics seriously affects the accuracy of numerical results near the boundary. The fictitious node method can modify the surface effect of peridynamics, but the previous method (Le and Bobaru, 2018) is only applicable to problems with only stress boundary conditions. This paper proposes an extended fictitious node method for deriving the fictitious node displacement constraint equations that apply to the displacement boundary conditions, based on the corresponding equivalence of stress components along with the boundary normal and tangential directions on the left and right sides of the boundary node. Consequently, the extended fictitious node method can handle problems with mixed boundary conditions of stress and displacement constraints. Then, this method is verified through numerical examples with mixed boundary conditions. The results after the surface correction show good agreements with those of the finite element method or with analytical solutions.