Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.

A symmetric substructuring method for analyzing the natural frequencies of conical origami structures

Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.

Analysis and Inverse Substructuring Computation on Dynamic Quality of Mechanical Assembly

Mechanical assembly has its own dynamic quality directly affecting the dynamic quality of whole product and should be considered in quality inspection and estimation of mechanical assembly. Based on functional relations between dynamic characteristics involved in mechanical assembly, the effects of assembling process on dynamic characteristics of substructural components of an assembly system are investigated by substructuring analysis. Assembly-coupling dynamic stiffness is clarified as the dominant factor of the effects and can be used as a quantitative measure of assembly dynamic quality. Two computational schemes using frequency response functions（FRFs） to determine the stiffness are provided and discussed by inverse substructuring analysis, including their applicable conditions and implementation procedure in application. Eigenvalue analysis on matrix-ratios of FRFs before and after assembling is employed and well validates the analytical outcomes and the schemes via both a lumped-parameter model and its analogic experimental counterpart. Applying the two schemes to inspect the dynamic quality provides the message of dynamic performance of the assembly system, and therefore improves conventional quality inspection and estimation of mechanical assembly in completeness.

DYNAMIC SUBSTRUCTURING ANALYSISOF COMPOSITE STRUCTURES WITHNONLINEAR LINKS

The paper deals with the dynamic response prediction of the composite structure,which consists of two linear components coupled by some nonlinear vibration isolators. Based on the measured impulse response functions of the linear components, three kinds of dynamic equations of interfacial integration are proposed and a procedure to transform the dynamic equations of integral type into a set of ordinary differential equations is suggested. Computer simulations and a real test are given to verify the effectiveness of the theoretical results.

Dynamic environmentprediction of spacecraft usingdynamic substructuring

A low frequency dynamic environment prediction of spacecraft using dynamic substructu- ring is presented. The dynamic environment could be used to describe the level of the excitation on the spacecraft itself and auxiliary equipment. In addition, the dynamic environment is a criterion for the structural dynamic design as well as the ground verification test. The proposed prediction method could solve two major problems. The first is the time consumption of analyzing the whole spacecraft model due to the huge amount of degrees of freedom, and the second is multi-source for component structural dynamic models from distributive departments. To demonstrate the feasibility and efficien- cy, the proposed prediction method is applied to resolve a launching satellite case, and the results were compared with those obtained by the traditional prediction technology using the finite element method.

DSAS:A new macromolecular substructure solution program based on the modified phase-retrieval algorithm

Considering the pivotal role of single-wavelength anomalous diffraction(SAD) in macromolecular crystallography,our objective was to introduce DSAS,a novel program designed for efficient anomalous scattering substructure determination.DSAS stands out with its core components:a modified phase-retrieval algorithm and automated parameter tuning.The software boasts an intuitive graphical user interface(GUI),facilitating seamless input of essential data and real-time monitoring.Extensive testing on DSAS has involved diverse datasets,encompassing proteins,nucleic acids,and various anomalous scatters such as sulfur(S),selenium(Se),metals,and halogens.The results confirm DSAS’s exceptional performance in accurately determining heavy atom positions,making it a highly effective tool in the field.

Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

Substructuring Technique for Dynamics Analysis of Flexible Beams with Large Deformation

In this paper, the substructuring technique is extended for the dynamics simulation of flexible beams with large deformation. The dynamics equation of a spatial straight beam undergoing large displacement and small deformation is deduced by using the Jourdain variation principle and the model synthesis method. The longitudinal shortening effect due to the transversal deformation is taken into consideration in the dynamics equation. In this way, the geometric stiffening effect, which is also called stress stiffening effect, is accounted for in the dynamics equation. The transfer equation of the flexible beam is obtained by assembling the dynamics equation and the kinematic relationship between the two connection points of the flexible beam. Treating a flexible beam with small deformation as a substructure, one can solve the dynamics of a flexible beam with large deformation by using the substructuring technique and the transfer matrix method. The dynamics simulation of a flexible beam with large deformation is carried out by using the proposed approach and the results are verified by comparing with those obtained from Abaqus software.

An efficient method for train-track-substructure dynamic interaction analysis by implicit-explicit integration and multi-time-step solution

In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solution method(abbreviated as mI-nE-MTS method).The TTS system is divided into train-track subsystem and substruc-ture subsystem.Considering that the root cause of low effi-ciency of obtaining TTS solution lies in solving the alge-braic equation of the substructures,the high-efficient Zhai method,an explicit integration scheme,can be introduced to avoid matrix inversion process.The train-track system is solved by implicitly Park method.Moreover,it is known that the requirement of time step size differs for different sub-systems,integration methods and structural frequency response characteristics.A multi-time-step solution is pro-posed,in which time step size for the train-track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand,namely the time spent for m implicit integral steps is equal to n explicit integral steps,i.e.,mI=nE as mentioned above.The numeri-cal examples show the accuracy,efficiency,and engineering practicality of the proposed method.

Morphogenesis of Floating Bone Segments: A Legacy of Serial Tensile Cross-Strut Microdamage in Trabecular Disconnection “Crumple Zones”?

Trabecular bone disconnection “hotspots” of real termini (ReTm) previously mapped as loci of weakness in the female aging spine and hip may be a source of free-floating cancellous segments found in the medullary space using a bespoke, thick slice histological method for identifying ReTm. A factor in their origin is apparently microdamage proliferation (differentiated by en bloc silver staining) with occasional callus moderation. Validation of similar “floating segments” (FS) in the ex-breeder rat suggested a pilot model for a potentially common phenomenon. Following marrow elution and density fractionation of the isolated floating segments from the whole proximal rat femora, scanning electron microscopy (SEM) and elemental microanalysis (EDS) was performed. The eluent contained numbers of vertically truncated, laterally branched floating segments (acute severance of sequential tensile cross-struts, causing chronic compression overload of axial-struts, with ii) inadequate stabilising callus, facilitating ReTm stacking into predetermined, substructural “crumple zones” of force containment, spheroidal attrition and particulate dissociation. As a catabolic outcome of altered tensile and hormonal influence, FS number may add a novel variable to cancellous bone kinetics particularly in women of relevance to fracture predisposition.

Survival Analysis Using Cox Proportional Hazards Regression for Pile Bridge Piles Under Wet Service Conditions

This paper studies the deterioration of bridge substructures utilizing the Long-Term Bridge Performance(LTBP)Program InfoBridge^(TM)and develops a survival model using Cox proportional hazards regression.The survival anal­ysis is based on the National Bridge Inventory(NBI)dataset.The study calculates the survival rate of reinforced and prestressed concrete piles on bridges under marine conditions over a 29-year span(from 1992 to 2020).The state of Maryland is the primary focus of this study,with data from three neighboring regions,the District of Columbia,Vir­ginia,and Delaware to expand the sample size.The data obtained from the National Bridge Inventory are condensed and filtered to acquire the most relevant information for model development.The Cox proportional hazards regres­sion is applied to the condensed NBI data with six parameters:Age,ADT,ADTT,number of spans,span length,and structural length.Two survival models are generated for the bridge substructures:Reinforced and prestressed concrete piles in Maryland and reinforced and prestressed concrete piles in wet service conditions in the District of Columbia,Maryland,Delaware,and Virginia.Results from the Cox proportional hazards regression are used to construct Markov chains to demonstrate the sequence of the deterioration of bridge substructures.The Markov chains can be used as a tool to assist in the prediction and decision-making for repair,rehabilitation,and replacement of bridge piles.Based on the numerical model,the Pile Assessment Matrix Program(PAM)is developed to facilitate the assessment and main­tenance of current bridge structures.The program integrates the NBI database with the inspection and research reports from various states’department of transportation,to serve as a tool for condition state simulation based on mainte­nance or rehabilitation strategies.

Effect of minor Sc and Zr addition on microstructure and properties of ultra-high strength aluminum alloy

The Al-9Zn-2.8Mg-2.5Cu-xZr-ySc alloys （x=0, 0.15%, 0.15%; y=0, 0.05%, 0.15%）, produced by low-frequent electromagnetic casting technology, were subjected to homogenization treatment, hot extrusion, solution and aging treatment. The effects of minor Sc and Zr addition on microstructure, recrystallization and properties of alloys were studied by optical microscopy （OM）, scanning electron microscopy （SEM） and transmission electron microscopy （TEM）. The results show that Sc and Zr addition can refine grains of the as-cast alloy by precipitation of primary Al3（Sc,Zr） particles formed during solidification as heterogeneous nuclei. Secondary Al3（Sc,Zr） precipitates formed during homogenization treatment strongly pin the movement of dislocation and subgrain boundaries, which can effectively inhibit the alloys recrystallization. Compared with the alloy without Sc and Zr addition, the Al-Zn-Mg-Cu-Zr alloy with 0.05%Sc and 0.15%Zr shows the increase in tensile strength and yield strength by 172 MPa and 218 MPa, respectively. Strengthening comes from the contributions of precipitation, substructure and grain refining.

Research on Rice Panicle L-system Model Based on Substructure Algorithm

In order to decrease model complexity of rice panicle for its complicated morphological structure,an interactive L-system based on substructure algorithm was proposed to model rice panicle in this study.Through the analysis of panicle morphology,the geometrical structure models of panicle spikelet,axis and branch were constructed firstly.Based on that,an interactive panicle L-system model was developed by using substructure algorithm to optimize panicle geometrical models with the similar structure.Simulation results showed that the interactive L-system panicle model based on substructure algorithm could fast construct panicle morphological structure in reality.In addition,this method had the well reference value for other plants model research.

DESIGN OF WAVE-SHAPED SPACE TRUSS CONSIDERING THE EFFECT OF SUBSTRUCTURE

The wave-shaped space truss is used as the roof of the natatorium in Tianjin University,which ingeniously displays the function of the building.In this paper,the wave-shaped space truss is analyzed and designed,considering the substructure made of reinforced concrete rigid frame and the space truss working together.Also,the anti-seismic characteristic of the wave-shaped space truss is studied based on the integral model.

Seismic wave input method for three-dimensional soil-structure dynamic interaction analysis based on the substructure of artificial boundaries

The method of inputting the seismic wave determines the accuracy of the simulation of soil-structure dynamic interaction. The wave method is a commonly used approach for seismic wave input, which converts the incident wave into equivalent loads on the cutoff boundaries. The wave method has high precision, but the implementation is complicated, especially for three-dimensional models. By deducing another form of equivalent input seismic loads in the fi nite element model, a new seismic wave input method is proposed. In the new method, by imposing the displacements of the free wave fi eld on the nodes of the substructure composed of elements that contain artifi cial boundaries, the equivalent input seismic loads are obtained through dynamic analysis of the substructure. Subsequently, the equivalent input seismic loads are imposed on the artifi cial boundary nodes to complete the seismic wave input and perform seismic analysis of the soil-structure dynamic interaction model. Compared with the wave method, the new method is simplifi ed by avoiding the complex processes of calculating the equivalent input seismic loads. The validity of the new method is verifi ed by the dynamic analysis numerical examples of the homogeneous and layered half space under vertical and oblique incident seismic waves.

Kinetostatic Modeling and Analysis of an Exechon Parallel Kinematic Machine(PKM) Module

As a newly invented parallel kinematic machine（PKM）, Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method（FEM）. The equilibrium equations of the platform are derived with Newton＇s 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system＇s deflections. The platform＇s elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.

Simulation of large-scale numerical substructure in real-time dynamic hybrid testing

A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element （FE） numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom （DOFs）. Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.

Model updating for real time dynamic substructures based on UKF algorithm

Combining the advantages of numerical simulation with experimental testing,real-time dynamic substructure(RTDS)testing provides a new experimental method for the investigation of engineered structures.However,not all unmodeled parts can be physically tested,as testing is often limited by the capacity of the test facility.Model updating is a good option to improve the modeling accuracy for numerical substructures in RTDS.In this study,a model updating method is introduced,which has great performance in describing this nonlinearity.In order to determine the optimal parameters in this model,an Unscented Kalman Filter(UKF)-based algorithm was applied to extract the knowledge contained in the sensors data.All the parameters that need to be identified are listed as the extended state variables,and the identification was achieved via the step-by-step state prediction and state update process.Effectiveness of the proposed method was verified through a group of experimental data,and results showed good agreement.Furthermore,the proposed method was compared with the Extended Kalman Filter(EKF)-based method,and better accuracy was easily found.The proposed parameter identification method has great applicability for structural objects with nonlinear behaviors and could be extended to research in other engineering fields.

Impact of Zener-Hollomon parameter on substructure and texture evolution during thermomechanical treatment of iron-containing wrought aluminium alloys

The objective of the investigation is to evaluate the influence of the Zener-Hollomon parameter on substructure and texture evolution in iron-containing wrought aluminium alloys (type AA8011). Methods applied are X-ray texture analysis, electron backscatter diffraction (EBSD) and optical microscopy. The results show a serious impact of the Zener-Hollomon parameter on cube texture evolution during the thermomechanical treatment in iron-containing aluminium alloys. An increase in the Zener-Hollomon parameter reduces the survivability of cube texture during hot deformation and reinforces particle-stimulated nucleation (PSN) during the annealing process. However, thermomechanical treatment at low temperatures leads to active precipitation and as a result fine-dispersed participles tend to block all nuclei except for those producing large cube-oriented grains. It is concluded that in iron-containing wrought aluminium alloys, the general correlation between the Zener-Hollomon parameter and subgrain size is similar to that observed in 3xxx series alloys and can be described by the specific set of equations derived.

Nucleation of recrystallization in magnesium alloy grains of varied orientation and the impacts on texture evolution

Selection of appropriate thermomechanical processing parameters is crucial for control of the crystallographic texture and grain size distribution in wrought magnesium alloys, which in turn dictate their mechanical properties. In this work, the recrystallization behavior of binary Mg-Zn alloys are examined after warm rolling as a function of alloy content and heat treatment temperature. The Avrami exponent increased with increasing heat treatment temperature up to the Mg Zn solvus, while the strength of the recrystallization texture decreased.Neither the Avrami exponent nor the qualitative trends in texture evolution were sensitive to the Zn alloying content in the examined range.EBSD and transmission electron microscopy observations revealed that the changes in texture and recrystallization kinetics could be attributed to differences in the nucleation behavior of basal and off-basal orientations.