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NONLINEAR RESPONSE AND STABILITY ANALYSIS OF BEAMS USING FINITE-ELEMENTS IN TIME

AIAA JOURNAL 1988年第9期26卷 1135-1142页

作者： BAUCHAU, OA HONG, CH Rensselaer Polytechnic Institute Troy New York

The dynamic response and stability analysis of beams undergoing large deflections and rotations is analyzed using the finite-element method in time. This formulation provides an efficient and consistent approach to predicting the dynamic response of nonlinear periodic systems as well as their stability boundaries based on Floquet’s theory. This paper has two goals: 1) to present the formulation of the finite element in time equations for naturally curved and twisted beams undergoing large deflections and rotations, and 2) to discuss the predictions of this method when applied to several classical nonlinear beam problems for which analytical solutions exist and, in some cases, experimental results are available. These examples are 1) the natural vibration frequencies of a rotating beam, 2) the harmonic and superharmonic response of a clamped-clamped beam undergoing largeamplitude vibrations, 3) the dynamic instability of a cantilevered beam under a tip follower force, and 4) the parametric excitation of a beam under an axial pulsating load, with and without the presence of viscous damping forces. In all cases, close agreement is found between the analytical results and the predictions of the finite element in time approach, which appears to be an efficient and reliable technique for nonlinear dynamic response and stability analysis of periodic systems. © 1988 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Finite Element Modeling Dynamic Response Harmonic Response Cantilever Beam Kinetic Energy integration algorithm Bending Stiffness Nonlinear Systems

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Multiscale modeling of diffuse damage and localized cracking in quasi-brittle materials under compression with a quadratic friction law

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2024年 304卷

作者： Zhao, Lun-Yang Ren, Lu Liu, Ling-Hui Lai, Yuan-Ming Niu, Fu-Jun You, Tao South China Univ Technol South China Inst Geotech Engn Sch Civil Engn & Transportat Guangzhou 510641 Peoples R China South China Univ Technol State Key Lab Subtrop Bldg & Urban Sci Guangzhou 510641 Peoples R China Univ Leoben Dept Geoenergy A-8700 Leoben Austria

The diffuse damage and localized cracking of quasi-brittle materials ( i.e. , rocks and concretes) under compression can be delineated by a matrix-microcrack system, wherein a solid matrix phase is weakened by a large number of randomly oriented and distributed microcracks, and the macroscopic cracking is formed by a progressive evolution of microcracks. Several homogenization-based multiscale models have been proposed to describe this matrix-microcrack system, but most of them are based on a linear friction law on the microcrack surface, rendering a linear strength criterion. In this paper, we propose a new quadratic friction law within the local multiscale friction-damage (LMFD) model to capture the plastic distortion due to frictional sliding along the rough microcrack surface. Following that, a macroscopic Ottosen-type nonlinear strength criterion is rationally derived with up-scaling friction-damage coupling analysis. An enhanced semi-implicit return mapping (ESRM) algorithm with a substepping scheme is then developed to integrate the complex nonlinear constitutive model. The performance of LMFD model is evaluated compared to a wide range of experimental data on plain concretes, and the robustness of ESRM algorithm is assessed through a series of numerical tests. Subsequently, to effectively describe the localized cracking process, a regularization scheme is proposed by combining the phase-field model with the established LMFD model, and the discretization independent crack localization is numerically verified.

关键词： Quasi-brittle materials Homogenization-based multiscale modeling Quadratic friction law integration algorithm Phase-field model

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Bayesian Approach to Quantifying Epistemic Uncertainty in a Processor Availability Model

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JOURNAL OF SPACECRAFT AND ROCKETS 2012年第6期49卷 1019-1031页

作者： Everline, Chester J. CALTECH Jet Prop Lab Pasadena CA 91109 USA

It is often necessary to use a combination of testing and analysis to demonstrate compliance with quantitative performance requirements. Increasingly, the demonstration must establish that requirements are satisfied with a certain level of confidence. As an example, a processor intended for space applications may be required to have a certain reliability or availability (e.g., at least 99.9%) with high confidence (e.g., 95%). This paper examines the application of Bayesian statistics and Monte Carlo simulation to such situations, focusing on quantifying epistemic uncertainty associated with the quantity of available data, the validity of alternative models, probabilistically combining alternative models when appropriate, and estimating epistemic uncertainty associated with certain aspects of model completeness.

关键词： Bayesian Approach Probability Density Functions Monte Carlo Simulation Gamma Function Flight Testing integration algorithm Numerical Simulation Flight Operation Fault Injection Micrometeoroids

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A New Graph Autoencoder-Based Consensus-Guided Model for scRNA-seq Cell Type Detection

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024年第2期35卷 2473-2483页

作者： Zhang, Dai-Jun Gao, Ying-Lian Zhao, Jing-Xiu Zheng, Chun-Hou Liu, Jin-Xing Qufu Normal Univ Sch Comp Sci Rizhao 276826 Shandong Peoples R China Qufu Normal Univ Qufu Normal Univ Lib Rizhao 276826 Shandong Peoples R China

Single-cell RNA sequencing (scRNA-seq) technology is famous for providing a microscopic view to help capture cellular heterogeneity. This characteristic has advanced the field of genomics by enabling the delicate differentiation of cell types. However, the properties of single-cell datasets, such as high dropout events, noise, and high dimensionality, are still a research challenge in the single-cell field. To utilize single-cell data more efficiently and to better explore the heterogeneity among cells, a new graph autoencoder (GAE)-based consensus-guided model (scGAC) is proposed in this article. The data are preprocessed into multiple top-level feature datasets. Then, feature learning is performed by using GAEs to generate new feature matrices, followed by similarity learning based on distance fusion methods. The learned similarity matrices are fed back to the GAEs to guide their feature learning process. Finally, the abovementioned steps are iterated continuously to integrate the final consistent similarity matrix and perform other related downstream analyses. The scGAC model can accurately identify critical features and effectively preserve the internal structure of the data. This can further improve the accuracy of cell type identification.

关键词： Feature extraction Representation learning Genetic algorithms Sequential analysis Optimization Data models Mathematical models Distance fusion graph autoencoder (GAE) integration algorithm single-cell RNA-seq

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On the increase of computational algorithm efficiency for elasto-plastic shell analysis

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ENGINEERING COMPUTATIONS 1997年第1期14卷 75-&页

作者： Soric, J Montag, U Kratzig, WB Institut für Statik und Dynamik Ruhr‐Universität Bochum Germany

Presents a robust and unconditionally stable return-mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elastoplastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four-node isoparametric assumed-strain finite-rotation shell element employing the Mindlin-Reissner-type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non-linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non-linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.

关键词： consistent tangent modulus finite element analysis elasto-plastic behaviour integration algorithm shell structures tangent matrices

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EXPLICIT-IMPLICIT STAGGERED PROCEDURE FOR MULTIBODY DYNAMICS ANALYSIS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1990年第3期13卷 562-570页

作者： PARK, KC CHIOU, JC DOWNER, JD UNIV COLORADO CTR SPACE STRUCT & CONTROLS BOULDER CO 80309 USA

An explicit-implicit staggered time-integration procedure is presented for the solution of multibody dynamical equations involving large rotations and constraints. The algorithms adopts a two-stage modification of the central difference algorithm for integrating the translational coordinates and the angular velocity vector, and the midpoint implicit algorithm to solve the kinematical relation in terms of the Euler parameters for updating the angular orientations. The Lagrange multipliers to enforce the system constraints are obtained by implicitly integrating a parabolically regularized differential equation for the multipliers. The performance of the present procedure has been evaluated to applying the procedure to solve several sample problems. The results indicate that the procedure is robust in dealing with a variety of constraints and spatial kinematic motions, hence it is recommended for applications to general multibody dynamics analyses. (Author)

关键词： Multibody Dynamics Numerical integration integration algorithm Linkages Transient Response Holonomic Constraints Computing Large Space Structures Software Architecture Simulation Software

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Third-order, minimal-parameter solution of the orthogonal matrix differential equation

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1997年第3期20卷 516-521页

作者： Ronen, M Oshman, Y Technion—Israel Institute of Technology Haifa 32000 Israel

The problem of minimal-parameter solution of the orthogonal matrix differential equation is addressed. This well-known equation arises naturally in three-dimensional attitude determination problems (in aircraft and satellite navigation systems), as well as in the square-root solution of the matrix Riccati differential equation. A direct solution of this equation involves n(2) integrations for the elements of the nth-order solution matrix. However, since an orthogonal matrix is determined by only n(n - 1)/2 independent (albeit nonunique) parameters, a much more efficient solution may, conceivably, be obtained by a parametrization of the problem in terms of such parameters. A new, third-order minimal parametrization, which is motivated by the Peano-Baker solution of linear matrix differential equations, is introduced. The parameters and their corresponding differential equation are very simple and natural. The proposed method is used to provide a new derivation of a closed-form third-order quaternion propagation algorithm, which is commonly used in strapdown inertial navigation systems utilizing rate-integrating gyros. A numerical example is used to demonstrate the viability and high efficiency of the new algorithm.

关键词： Differential Equations Quaternions Strapdown Inertial Navigation System Satellite Navigation Systems Euler Angles Runge Kutta integration integration algorithm Riccati Equations FORTRAN Numerical algorithms

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Heat transfer in a homogeneous suspension including radiation and history effects

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1998年第3期12卷 304-312页

作者： Coimbra, CFM Edwards, DK Rangel, RH Univ Calif Irvine Dept Mech & Aerosp Engn Irvine CA 92697 USA Univ Calif Irvine Dept Chem & Biochem Engn & Mat Sci Irvine CA 92697 USA

An analytical formulation of the thermal response of particles subjected to time-dependent temperature perturbations in the surrounding medium is presented. The suspension of particles is considered homogeneous and dilute. The continuous medium containing the dispersion of particles is assumed to be weakly participating, having a small but nonzero absorption coefficient. The particles in suspension are small, so that the mechanisms of heat transfer between the particles and the continuous phase are conduction and radiation only. The general solution for the temperature response of the particles to time-dependent perturbations in the continuous phase is derived for the limit of small Biot and infinitesimal Peclet numbers. The method used to derive the general solution consists of including the linearized radiation effects in the integro-differential equation that describes the temperature history of the particles. A fractional-differential operator that contains a Riemann-Liouville-Weyl half-derivative term is then applied to the radiation-diffusion equation to render the governing equation analytically tractable. The resulting equation is solved exactly by the method of variation of parameters. Linear and harmonic perturbations are analyzed and discussed, and the radiative and history term contributions to the temperature response of the particles are studied.

关键词： Heat Transfer Enhancement Thermal Diffusivity Peclet Numbers Thermal Response Radiation Heat Transfer Heat Capacity Ratio Stefan Boltzmann Constant Optical Properties integration algorithm Numerical integration

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Family of constraint-preserving integrators for solving quaternion equations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2001年第1期24卷 72-78页

作者： Chiou, JC Jan, YR Wu, SD Natl Chiao Tung Univ Dept Elect & Control Engn Hsinchu 30010 Taiwan Precis Instrument Dev Ctr Div Res & Dev Hsinchu 30010 Taiwan

A family of numerical time integrators that exactly preserve the constraint of quaternion equations is developed, The constraint-preserving integrators based on the property of the skew-symmetric matrix and the proposed proven theorems are used to improve the accuracy of updating Euler parameters. The stability and accuracy analysis of the generalized constraint-preserving integrators is also discussed. Furthermore, we demonstrate that the proposed integrators are A-stable integrators that are proven to be useful in calculating angular orientations of kinematic and dynamic systems. A numerical example is used to demonstrate the superiority of the proposed integrators.

关键词： Quaternions Inertial Measurement Unit integration algorithm Numerical Simulation Taylor Series Runge Kutta Methods Kinematic Analysis Dynamic Analysis Computing

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On nonisothermal elastoplastic analysis of shell components employing realistic hardening responses

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2001年第28-29期38卷 5019-5039页

作者： Tonkovic, Z Soric, J Krätzig, WB Univ Zagreb Fac Mech Engn & Naval Architecture Zagreb 10000 Croatia Ruhr Univ Bochum Inst Stat & Dynam D-44780 Bochum Germany

In the present paper, efficient numerical algorithms for elastoplastic analysis of shell-like structural components will be proposed employing nonisothermal, realistic, highly nonlinear hardening responses. The closest point projection integration algorithm is presented using a Reissner-Mindlin type kinematic shell model, completely formulated in tenser notation. Further, a consistent elastoplastic tangent modulus is derived, which ensures high convergence rates in the global iteration approach. The integration algorithm has been implemented into a layered assumed strain isoparametric finite element, which also enables geometrical nonlinearities including finite rotations. The nonisothermal elastoplastic response of a circular cylindrical shell and a box column under axial compression is analysed. Under the assumption of an adiabatic process, the increase in temperature is computed during elastoplastic deformation. Robustness and numerical stability of the proposed algorithms are demonstrated. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： shell structures finite element analysis elastoplasticity nonisothermal hardening responses integration algorithm tensor formulation

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