Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics

We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.

An Educational GUI-Based Software for Dynamic Analysis of Framed Structural Models

This paper introduces a new version of the open-source educational software, LESM (Linear Elements Structure Model), developed in MATLAB for structural analysis of one-dimensional models such as frames, trusses, and grillages. The updated program includes dynamic analysis, which incorporates inertial and damping effects, time-dependent load conditions, and a transient solver with multiple time integration schemes. The software assumes small displacements and linear-elastic material behavior. The paper briefly explains the theoretical basis for these developments and the reorganization of the source code using Object-Oriented Programming (OOP). The updated Graphical User Interface (GUI) allows interactive use of dynamic analysis features and displays new results such as animations, envelope diagrams of internal forces, phase portraits, and the response of degrees-of-freedom in time and frequency domain. The new version was used in a structural dynamics course, and new assignments were elaborated to improve students’ understanding of the subject.

ACG-TypeMethod for InverseQuadratic Eigenvalue Problems in Model Updating of Structural Dynamics

In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices M,D and K for the quadratic pencil Q(λ)=λ^(2)M+λD+K,so that Q(λ)has a prescribed subset of eigenvalues and eigenvectors.This method can determine the solvability of the inverse eigenvalue problem automatically.We then consider the least squares model for updating a quadratic pencil Q(λ).More precisely,we update the model coefficient matrices M,C and K so that(i)the updated model reproduces the measured data,(ii)the symmetry of the original model is preserved,and(iii)the difference between the analytical triplet(M,D,K)and the updated triplet(M_(new),D_(new),K_(new))is minimized.In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.

A strategy for lightweight designing of a railway vehicle car body including composite material and dynamic structural optimization

Rolling stock manufacturers are finding structural solutions to reduce power required by the vehicles,and the lightweight design of the car body represents a possible solution.Optimization processes and innovative materials can be combined in order to achieve this goal.In this framework,we propose the redesign and optimization process of the car body roof for a light rail vehicle,introducing a sandwich structure.Bonded joint was used as a fastening system.The project was carried out on a single car of a modern tram platform.This preliminary numerical work was developed in two main steps:redesign of the car body structure and optimization of the innovated system.Objective of the process was the mass reduction of the whole metallic structure,while the constraint condition was imposed on the first frequency of vibration of the system.The effect of introducing a sandwich panel within the roof assembly was evaluated,focusing on the mechanical and dynamic performances of the whole car body.A mass saving of 63%on the optimized components was achieved,corresponding to a 7.6%if compared to the complete car body shell.In addition,a positive increasing of 17.7%on the first frequency of vibration was observed.Encouraging results have been achieved in terms of weight reduction and mechanical behaviour of the innovated car body.

Solid-state NMR spectroscopy at ultrahigh resolution for structural and dynamical studies of MOFs

To characterize the structure and dynamics of metal--organic frameworks(MOFs)indepth at the molecular level,it is necessary to pursue high-resolution solid-state magic angle spinning(MAS)nuclear magnetic resonance(NMR)spectroscopy.Spectral resolution is usually affected by the quality of materials and various experimental conditions,of which magic angle(MA)accuracy is a crucial determinant.The current industrial criteria for MA calibration based on the common standard of KBr were found insufficient in guaranteeing optimal resolution MAS NMR for highly ordered MOFs.To drive towards higher-resolution MAS NMR spectroscopy,we propose_a calibration protocol for more accurate MA with a higher-precision criterion based on 79Br MAS NMR of KBr,where the linewidth ratio of the fifth-order spinning sideband to the central band of KBr should be less than 1.00.As a result,ultrahigh-resolution 13C cross-polarization(CP)MAS NMR of MOF-5 is achieved with minimal linewidths as low as 4 Hz,and therefore MOF-5 can be used as a new standard convenient for verifying MA accuracy and also optimizing 13c CP conditions.Maintaining high-precision MA under variable temperature(VT)was found challenging on certain commercial MAS NMR probes,as was systematically investigated by VT NMR using KBr and MOF-5.Nevertheless,ultrahigh-resolution MAS NMR spectroscopy with stable MA under VT is employed to reveal fine structures and linker dynamics of a series of Zn-based MOFs with highly regulated structures.The ultrahigh-resolution NMR methodcan be generally applied to study a broad range of MOFs and other materials.

Capturing the non-equilibrium state in light–matter–free-electron interactions through ultrafast transmission electron microscopy

Ultrafast transmission electron microscope(UTEM) with the multimodality of time-resolved diffraction, imaging,and spectroscopy provides a unique platform to reveal the fundamental features associated with the interaction between free electrons and matter. In this review, we summarize the principles, instrumentation, and recent developments of the UTEM and its applications in capturing dynamic processes and non-equilibrium transient states. The combination of the transmission electron microscope with a femtosecond laser via the pump–probe method guarantees the high spatiotemporal resolution, allowing the investigation of the transient process in real, reciprocal and energy spaces. Ultrafast structural dynamics can be studied by diffraction and imaging methods, revealing the coherent acoustic phonon generation and photoinduced phase transition process. In the energy dimension, time-resolved electron energy-loss spectroscopy enables the examination of the intrinsic electronic dynamics of materials, while the photon-induced near-field electron microscopy extends the application of the UTEM to the imaging of optical near fields with high real-space resolution. It is noted that light–free-electron interactions have the ability to shape electron wave packets in both longitudinal and transverse directions, showing the potential application in the generation of attosecond electron pulses and vortex electron beams.

Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

A global interpolating meshless shape function based on the generalized moving least-square(GMLS) is formulated by the transformation technique. Both the shape function and its derivatives meet the Kronecker delta function property. With the interpolating GMLS(IGMLS) shape function, an improved element-free Galerkin(EFG)method is proposed for the structural dynamic analysis. Compared with the conventional EFG method, the obvious advantage of the proposed method is that the essential boundary conditions including both displacements and derivatives can be imposed by the straightforward way. Meanwhile, it can greatly improve the ill-condition feature of the standard GMLS approximation, and provide good accuracy at low cost. The dynamic analyses of the Euler beam and Kirchhoff plate are performed to demonstrate the feasibility and effectiveness of the improved method. The comparison between the numerical results of the conventional method and the improved method shows that the proposed method has better stability, higher accuracy, and less time consumption.

Seismic response of a mid-story isolated structure considering SSI in mountainous areas under long-period earthquakes

At present,there is not much research on mid-story isolated structures in mountainous areas.In this study,a model of a mid-story isolated structure considering soil-structure interaction(SSI)in mountainous areas is established along with a model that does not consider SSI.Eight long-period earthquake waves and two ordinary earthquake waves are selected as inputs for the dynamic time history analysis of the structure.The results show that the seismic response of a mid-story isolated structure considering SSI in mountainous areas can be amplified when compared with a structure that does not consider SSI.The structure response under long-period earthquakes is larger than that of ordinary earthquakes.The structure response under far-field harmonic-like earthquakes is larger than that of near-fault pulse-type earthquakes.The structure response under near-fault pulse-type earthquakes is larger than that of far-field non-harmonic earthquakes.When subjected to long-period earthquakes,the displacement of the isolated bearings exceeded the limit value,which led to instability and overturning of the structure.The structure with dampers in the isolated story could adequately control the nonlinear response of the structure,effectively reduce the displacement of the isolated bearings,and provide a convenient,efficient and economic method not only for new construction but also to retrofit existing structures.

Graph Convolutional Networks Embedding Textual Structure Information for Relation Extraction

Deep neural network-based relational extraction research has made significant progress in recent years,andit provides data support for many natural language processing downstream tasks such as building knowledgegraph,sentiment analysis and question-answering systems.However,previous studies ignored much unusedstructural information in sentences that could enhance the performance of the relation extraction task.Moreover,most existing dependency-based models utilize self-attention to distinguish the importance of context,whichhardly deals withmultiple-structure information.To efficiently leverage multiple structure information,this paperproposes a dynamic structure attention mechanism model based on textual structure information,which deeplyintegrates word embedding,named entity recognition labels,part of speech,dependency tree and dependency typeinto a graph convolutional network.Specifically,our model extracts text features of different structures from theinput sentence.Textual Structure information Graph Convolutional Networks employs the dynamic structureattention mechanism to learn multi-structure attention,effectively distinguishing important contextual features invarious structural information.In addition,multi-structure weights are carefully designed as amergingmechanismin the different structure attention to dynamically adjust the final attention.This paper combines these featuresand trains a graph convolutional network for relation extraction.We experiment on supervised relation extractiondatasets including SemEval 2010 Task 8,TACRED,TACREV,and Re-TACED,the result significantly outperformsthe previous.

Mass-Stiffness Templates for Cubic Structural Elements Dedicated to Professor Karl Stark Pister for his 95th birthday

1 This paper considers Lagrangian finite elements for structural dynamics constructed with cubic displacement shape functions.The method of templates is used to investigate the construction of accurate mass-stiffness pairs.This method introduces free parameters that can be adjusted to customize elements according to accuracy and rank-sufficiency criteria.One-and two-dimensional Lagrangian cubic elements with only translational degrees of freedom(DOF)carry two additional nodes on each side,herein called side nodes or SN.Although usually placed at the third-points,the SN location may be adjusted within geometric limits.The adjustment effect is studied in detail using symbolic computations for a bar element.The best SN location is taken to be that producing accurate approximation to the lowest natural frequencies of the continuum model.Optimality is investigated through Fourier analysis of the propagation of plane waves over a regular infinite lattice of bar elements.Focus is placed on the acoustic branch of the frequency-vs.-wavenumber dispersion diagram.It is found that dispersion results using the fully integrated consistent mass matrix(CMM)are independent of the SN location whereas its lowfrequency accuracy order is O(κ8),whereκis the dimensionless wave number.For the diagonally lumped mass matrix(DLMM)constructed through the HRZ scheme,two optimal SN locations are identified,both away from third-points and of accuracy order O(κ8).That with the smallest error coefficient corresponds to the Lobatto 4-point integration rule.A special linear combination of CMM and DLMM with nodes at the Lobatto points yields an accuracy of O(κ10)without any increase in the computational effort over CMM.The effect of reduced integration(RI)on both mass and stiffness matrices is also studied.It is shown that singular mass matrices can be constructed with 2-and 3-point RI rules that display the same optimal accuracy of the exactly integrated case,at the cost of introducing spurious modes.The optimal SN location in two-dimensional,bicubic,isoparametric plane stress quadrilateral elements is briefly investigated by numerical experiments.The frequency accuracy of flexural modes is found to be fairly insensitive to that position,whereas for bar-like modes it agrees with the one-dimensional results.

Structural Parameter Analyses on Rotor Airloads with New Type Blade-Tip Based on CFD/CSD Coupling Method

For accurate aeroelastic analysis,the unsteady rotor flowfield is solved by computational fluid dynamics(CFD)module based on RANS/Euler equations and moving-embedded grid system,while computational structural dynamics(CSD)module is introduced to handle blade flexibility.In CFD module,dual time-stepping algorithm is employed in temporal discretization,Jameson two-order central difference(JST)scheme is adopted in spatial discretization and B-L turbulent model is used to illustrate the viscous effect.The CSD module is developed based on Hamilton′s variational principles and moderate deflection beam theory.Grid deformation is implemented using algebraic method through coordinate transformations to achieve deflections with high quality and efficiency.A CFD/CSD loose coupling strategy is developed to transfer information between rotor flowfield and blade structure.The CFD and the CSD modules are verified seperately.Then the CFD/CSD loose coupling is adopted in airloads prediction of UH-60A rotor under high speed forward flight condition.The calculated results agree well with test data.Finally,effects of torsional stiffness properties on airloads of rotors with different tip swept angles(from 10° forward to 30° backward)are investigated.The results are evaluated through pressure distribution and airloads variation,and some meaningful conclusions are drawn the moderated shock wave strength and pressure gradient caused by varied tip swept angle and structural properties.

Investigation of the Short-Time Photodissociation Dynamics of Furfural in S2 State by Resonance Raman and Quantum Chemistry Calculations

Raman(resonance Raman,FT-Raman),IR and UV-visible spectroscopy and quantum chemistry calculations were used to investigate the photodissociation dynamics of furfural in S2 state.The resonance Raman(RR)spectra indicate that the photorelaxation dynamics for the S0→S2 excited state is predominantly along nine motions:C=O stretchν5(1667 cm-1),ring C=C antisymmetric stretchν6(1570 cm-1),ring C=C symmetric stretchν7(1472 cm-1),C2-O6-C5 symmetric stretch/C1-H8 rock in planeν8(1389 cm-1),C3-C4 stretch/C1-H8 rock in planeν9(1370 cm-1),C5-O6 stretch in planeν12(1154 cm-1),ring breathν13(1077 cm-1),C3-C4 stretchν14(1020 cm-1),C3-C2-O6 symmetric stretchν16(928 cm-1).Stable structures of S0,S1,S2,T1 and T2 states with Cs point group were optimized at CASSCF method in Franck-Condon region there are S2/S1 conical intersection was found by state average method and RR spectra.

Numerical Analysis and Study of the Dynamic Response of Structural Systems for Machinery Foundations

This work aims the deterministic dynamic analysis,in the time and frequency domain,of a reinforced concrete floor supported by a pre-cast pile foundation system,when subjected to the excitation produced by a large compressor installed in an industry for the production of air gases.The concrete slab presents a dimension of 12 m×15 m,required to support a compressor-motor assembly weighting 1,900 kN and positioned at a height of 4m of the investigated concrete floor.In this investigation,two numerical models were developed and the difference between these models is characterized by the discretization of the support points(pre-cast concrete piles).The developed numerical model adopted the usual mesh refinement techniques present in finite element method simulations implemented in the CSi SAP2000 V.17.2.0 software.Based on the developed analysis methodology,the dynamic structural response of the foundation system is evaluated in terms of natural frequencies,vibration modes,displacements,velocities,and accelerations.The maximum values of the dynamic response of the system are compared with the limit values recommended by standards and project recommendations,aiming a careful evaluation,regarding the performance of the structure in terms of excessive vibrations and the economic aspects involved in the design of the foundation system.Finally,the obtained results of the two developed numerical models are compared,as to evaluate if there are benefits in refining the support points modelling.

A lumped mass Chebyshev spectral element method and its application to structural dynamic problems

A diagonal or lumped mass matrix is of great value for time-domain analysis of structural dynamic and wave propagation problems,as the computational efforts can be greatly reduced in the process of mass matrix inversion.In this study,the nodal quadrature method is employed to construct a lumped mass matrix for the Chebyshev spectral element method(CSEM).A Gauss-Lobatto type quadrature,based on Gauss-Lobatto-Chebyshev points with a weighting function of unity,is thus derived.With the aid of this quadrature,the CSEM can take advantage of explicit time-marching schemes and provide an efficient new tool for solving structural dynamic problems.Several types of lumped mass Chebyshev spectral elements are designed,including rod,beam and plate elements.The performance of the developed method is examined via some numerical examples of natural vibration and elastic wave propagation,accompanied by their comparison to that of traditional consistent-mass CSEM or the classical finite element method(FEM).Numerical results indicate that the proposed method displays comparable accuracy as its consistent-mass counterpart,and is more accurate than classical FEM.For the simulation of elastic wave propagation in structures induced by high-frequency loading,this method achieves satisfactory performance in accuracy and efficiency.

Numerical Simulation of ATPS Parachute Transient Dynamics Using Fluid-Structure Interaction Method

In order to simulate and analyze the dynamic characteristics of the parachute from advanced tactical parachute system(ATPS),a nonlinear finite element algorithm and a preconditioning finite volume method are employed and developed to construct three dimensional parachute fluid-structure interaction(FSI)model.Parachute fabric material is represented by membrane-cable elements,and geometrical nonlinear algorithm is employed with wrinkling technique embedded to simulate the large deformations of parachute structure by applying the NewtonRaphson iteration method.On the other hand,the time-dependent flow surrounding parachute canopy is simulated using preconditioned lower-upper symmetric Gauss-Seidel(LU-SGS)method.The pseudo solid dynamic mesh algorithm is employed to update the flow-field mesh based on the complex and arbitrary motion of parachute canopy.Due to the large amount of computation during the FSI simulation,massage passing interface(MPI)parallel computation technique is used for all those three modules to improve the performance of the FSI code.The FSI method is tested to simulate one kind of ATPS parachutes to predict the parachute configuration and anticipate the parachute descent speeds.The comparison of results between the proposed method and those in literatures demonstrates the method to be a useful tool for parachute designers.

Non-monotonic temperature evolution of nonlocal structure–dynamics correlation in CuZr glass-forming liquids

The structure–dynamics correlations in a nonlocal manner were investigated in CuZr metallic glass-forming liquids via classical molecular dynamics simulations.A spatial coarse-graining approach was employed to incorporate the nonlocal structural information of given structural order parameters in the structure–dynamics relationship.It is found that the correlation between structure order parameters and dynamics increases with increasing coarse-graining length and has a characteristic length scale.Moreover,the characteristic correlation length exhibits a non-monotonic temperature evolution as temperature approaches glass transition temperature,which is not sensitive to the considered structure order parameters.Our results unveil a striking change in the structure–dynamics correlation,which involves no fitting theoretical interpretation.These findings provide new insight into the structure–dynamics correlation in glass transition.

A symplectic finite element method based on Galerkin discretization for solving linear systems

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

Multi-layer analytic solution for k-ωmodel equations via a symmetry approach

Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting.Here,a multi-layer analytic expression is postulated for two lengths(stress and kinetic energy lengths),yielding an analytic solution for the k-ωmodel equations in pipe flow.Approximate local balance equations are analyzed to determine the key parameters in the solution,which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ωmodel,and hence the analytic construction is fully validated.The results provide clear evidence that the k-ωmodel sets in it a multilayer structure,which is similar to but different,in some insignificant details,from the Navier-Stokes(N-S)turbulence.This finding explains why the k-ωmodel is so popular,especially in computing the near-wall flow.Finally,the analysis is extended to a newlyrefined k-ωmodel called the structural ensemble dynamics(SED)k-ωmodel,showing that the SED k-ωmodel has improved the multi-layer structure in the outer flow but preserved the setting of the k-ωmodel in the inner region.

Astrophysical Applications of a Variant to Kepler’s Third Law

It is verified that the Nebula Hypothesis is applicable to the Solar System by way of a straightforward generalization of Kepler’s third law which also confirms that angular momentum transport is achieved by way of the self-gravity of the protoplanetary disk itself as it coalesces into planetesimals. The masses of the planets may then be approximately determined (within 10% error, for three planets) by way of this methodology, using the radius as well as the rate of rotation of the particular planet being considered. This would only be possible, not only in light of the Nebula Hypothesis, but also due to angular momentum transport (as these three planets most ideally express the expectations of angular momentum conservation from the protoplanetary disk). Also in this regard, the rotation of the Sun at its equator is discussed as it is found to be closely related to the planetary issue as it pertains to the evolution and structure of the body. A modified technique from that used in planetary study is then applied to the Galaxy for the purpose of the calculation of dark matter mass, presupposes treating the Galaxy as a homogeneous sphere (of dark matter) that is rotating. The model provides clear evidence of not only flat rotation-curves, but also the lack of centrifugal ejection of stars from galaxies as well as the configuration of the arms of spiral galaxies, along with a sound basis for black hole creation at the center of spiral galaxies.