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A consistent Timoshenko hysteretic beam finite element model

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2020年 119卷 103218-103218页

作者： Amir, M. Papakonstantinou, K. G. Warn, G. P. Penn State Univ Dept Civil & Environm Engn University Pk PA 16802 USA

A parametrized Timoshenko hysteretic beam finite element model is developed, using consistent two-node elements, to efficiently simulate the nonlinear behavior of structures. New displacement interpolation functions are derived that satisfy both the exact equilibrium and kinematic conditions. Therefore, nodal strain field continuity is achieved, resulting in a consistent formulation without shear locking effects. Multiaxial interactions are considered through yield/capacity functions and distributed plasticity is accounted for by appropriate hysteretic interpolation functions. The suggested interpolation functions yield constant element matrices that do not require updating throughout the analysis, and the nonlinearities are captured in terms of hysteretic curvatures, axial and shear deformations, which are set to evolve through ordinary differential equations. A computationally efficient solution scheme is also suggested, without requiring any linearization, to straightforwardly solve the resulting system of equations for quasi-static problems. The consistency, efficiency, versatility and validity of the suggested model is explained in detail and demonstrated through several numerical examples and comparisons with experimental data from available tests.

关键词： Hysteretic finite element Multiaxial interactions Distributed plasticity interpolation functions ODEs/DAEs

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Basis functions for residual stresses

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APPLIED MATHEMATICS AND COMPUTATION 2020年 386卷 125468-125468页

作者： Tiwari, Sankalp Chatterjee, Anindya Indian Inst Technol Dept Mech Engn Kanpur Uttar Pradesh India

We consider arbitrary preexisting residual stress states in arbitrarily shaped, unloaded bodies. These stresses must be self-equilibrating and traction free. Common treatments of the topic tend to focus on either the mechanical origins of the stress, or methods of stress measurement at certain locations. Here we take the stress field as given and consider the problem of approximating any such stress field, in a given body, as a linear combination of predetermined fields which can serve as a basis. We consider planar stress states in detail, and introduce an extremization problem that leads to a linear eigenvalue problem. Eigen-functions of that problem form an orthonormal basis for all possible residual stress states of sufficient smoothness. In numerical examples, convergence of the approximating stress fields is demonstrated in the L 2 norm for continuous stress fields as well as for a stress field with a simple discontinuity. Finally, we outline the extension of our theory to three dimensional bodies and states of stress. Our approach can be used to describe arbitrary preexisting residual stress states in arbitrarily shaped bodies using basis functions that are determined by the body geometry alone. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Residual stresses Basis functions interpolation functions

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The empirical optimal envelope and its application to local mean decomposition

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DIGITAL SIGNAL PROCESSING 2019年 87卷 166-177页

作者： Jia, Linshan Zhang, Qing Zheng, Xiang Yao, Pulin He, Xiaogao Wei, Xiaohan Xi An Jiao Tong Univ Sch Mech Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ Key Lab Educ Minist Modern Design & Rotor Bearing Syst Xian 710049 Peoples R China

Envelopes, which represent the overall information of the signal amplitude variation, are the necessary mediums in many signal decomposition methods. The phenomena of undershoot and overshoot result in the error of envelope estimation and unexpected signal decomposition components. In this paper, an accurate envelope estimation method, called the empirical optimal envelope (EOE), is proposed and applied to the local mean decomposition (LMD). First, an indicator of envelope distance is defined to describe the features of the ideal envelope. Utilizing the indicator, an iterative algorithm for the approximation of tangency points is designed. The tangency points, instead of the extreme points, are interpolated to realize the EOE. Then, the EOE is integrated with the LMD, and two interpolation functions, the cubic spline and the piecewise cubic Hermite interpolating polynomial, are combined to improve the efficiency and convergence of signal decomposition. Finally, the proposed method is verified by simulated signals and actual signals. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Empirical envelope Interpolated points interpolation functions Local mean decomposition

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Modified numerical approaches for a class of Volterra integral equations with proportional delays

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COMPUTATIONAL & APPLIED MATHEMATICS 2019年第2期38卷 1-19页

作者： Taghizadeh, Elham Matinfar, Mashallah Univ Mazandran Dept Math Babol Sar Iran

This paper addresses modified-meshless numerical schemes for dynamical systems with proportional delays. The proposed mesh reduction techniques are based on a redial-point interpolation and moving least-squares methods. An optimal influence domain radius is constructed utilizing nodal connectivity and node-depending integration background mesh. Optimal shape parameters are obtained by the use of properties of the delta Kronecker and the compactly supported weight function. Numerical results are provided to justify the accuracy and efficiency of the proposed schemes.

关键词： Functional calculus interpolation functions Meshless methods Radial point interpolation Moving least squares

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Some families of Genocchi type polynomials and their interpolation functions

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INTEGRAL TRANSFORMS AND SPECIAL functions 2012年第12期23卷 919-938页

作者： Srivastava, H. M. Kurt, Burak Simsek, Yilmaz Univ Victoria Dept Math & Stat Victoria BC V8W 3R4 Canada Akdeniz Univ Fac Sci Dept Math TR-07058 Antalya Turkey

The main purpose of this paper is to construct generating functions for some families of Genocchi type polynomials. By applying the derivative operator to these generating functions, we define a function which interpolates these polynomials at negative integers. Among other results, we prove a multiplication theorem for these polynomials. Furthermore, we give several other identities and applications associated with these and related polynomials and their interpolation functions.

关键词： generating functions Genocchi numbers Genocchi polynomials Euler numbers Euler polynomials Bernoulli numbers Bernoulli polynomials Apostol type polynomials Taylor-Maclaurin series expansions interpolation functions sums of powers of natural numbers multinomial coefficients Riemann zeta function Hurwitz (or generalized) zeta functions Hurwitz-Lerch zeta function

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Phase field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part I. General theory

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INTERNATIONAL JOURNAL OF PLASTICITY 2018年 106卷 164-185页

作者： Levitas, Valery I. Iowa State Univ Dept Aerosp Engn Ames IA 50011 USA Iowa State Univ Dept Mech Engn Ames IA 50011 USA Iowa State Univ Dept Mat Sci & Engn Ames IA 50011 USA Ames Lab Div Mat Sci & Engn Ames IA USA

Recently, results of molecular dynamics (MD) simulations were obtained for the crystal lattice instability conditions for the phase transformations (PTs) between semiconducting Si I and metallic Si II under action of all six components of the stress tensor (Levitas et al. (2017a, b)). These conditions are linear in terms of stresses normal to the cubic faces of Si I and are independent of the shear stresses. In the current paper, we (a) formulated the requirements for the thermodynamic potential and transformation deformation gradient tensors and (b) developed a phase field approach (PFA) for the stress-induced martensitic PTs for large strains while allowing for interfacial stresses, which are consistent with the obtained instability conditions. The general system of equations for coupled PFA and nonlinear elasticity is presented. Crystal lattice instability criteria are derived within a PFA, and it is proven that they are independent of the prescribed stress measure. In order to reproduce the lattice instability conditions obtained with MD: (a) one has to use the fifth degree polynomial interpolation functions of the order parameter for all material parameters;(b) each component of the transformation strain tensor should have a different interpolation functions;and (c) the interpolation functions for tensors of the elastic moduli of all ranks should have zero second derivatives for the parent and product phases, so that terms with elastic moduli, which are nonlinear in stresses, do not contribute to the lattice instability conditions. Specific interpolation and double-well functions have been derived for all parts of the Helmholtz free energy and for two models for the transformation deformation gradient. For these models, explicit expressions for the Ginzburg-Landau equations and lattice instability conditions are derived. Material parameters have been calibrated using results of MD simulations. In Part II of this paper, the developed model is further refined and

关键词： Phase-field approach Martensitic phase transformation Lattice instability condition interpolation functions Large strains

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Vibration analysis of multi-span lattice sandwich beams using the assumed mode method

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COMPOSITE STRUCTURES 2018年 185卷 716-727页

作者： Zhao, Zhao Wen, Shurui Li, Fengming Beijing Univ Technol Coll Mech Engn Beijing 100124 Peoples R China Harbin Engn Univ Coll Aerosp & Civil Engn Harbin 150001 Heilongjiang Peoples R China

So far, little attention has been paid to the vibration analysis of multi-span lattice sandwich beams, particularly using the assumed mode method (AMM). In this paper, the mode shapes of multi-span sandwich beams are assumed as those of uniform beams modified by the interpolation functions. The equation of motion of the beam is established using Hamilton's principle. The natural frequencies of multi-span pyramidal and Kagome sandwich beams so calculated agree well with those determined using the ANSYS software, which indicates that the present methodology is suitable for solving multi-span sandwich beams with lattice truss cores. The effects of Young's modulus, damping and geometric parameters of cores and sheets on the natural frequencies and time domain responses of two kinds of multi-span sandwich beams are analyzed. When the truss radius and sheet thickness are increased, the natural frequencies are increased initially and then decrease, while the vibration amplitudes at the mid-points of both the multi-span pyramidal and Kagome sandwich beams decrease. With the increase of the inclination angle of the truss alpha(c), the natural frequencies of structures experience a slight decline. In contrast, the amplitudes at the mid-points of the two different three-span sandwich beams both rise.

关键词： Multi-span lattice sandwich beam Free vibration analysis Assumed mode method interpolation functions Natural frequency

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Free vibration analysis of multi-span Timoshenko beams using the assumed mode method

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ARCHIVE OF APPLIED MECHANICS 2018年第7期88卷 1213-1228页

作者： Zhao, Zhao Wen, Shurui Li, Fengming Zhang, Chuanzeng Beijing Univ Technol Coll Mech Engn Beijing 100124 Peoples R China Harbin Engn Univ Coll Aerosp & Civil Engn Harbin 150001 Heilongjiang Peoples R China Univ Siegen Dept Civil Engn D-57068 Siegen Germany

Although some investigations on the vibration properties of multi-span beams have been conducted, studies on multi-span Timoshenko beams by using the assumed mode method have been relatively few. In this paper, the multi-span Timoshenko beams are investigated, and the mode shapes of the beams are modified by the interpolation functions to model the vibration modes of the multi-span beams. Hamilton's principle is applied to establish the equation of motion of the structure, and the natural circular frequencies and the free vibration responses of the multi-span beams are obtained. The numerical results demonstrate good agreement between the present results and those from the open literature and the ANSYS software. The influences of the length-thickness ratio, the disorder degree and the span number on the free vibration of the structure are also analyzed. It is observed that the displacement amplitude and the vibration period at the midpoint of the three-span Timoshenko beams are reduced when the disorder degree and the length-thickness ratio are reduced. The increase in the span number of the multi-span beams with equal spans leads to the decrease in the displacement amplitude and the period of the structures. Furthermore, some interesting phenomena are found, e.g., the same even-order frequencies of different three-span beams are equal under specific disorder degree.

关键词： Multi-span beam Assumed mode method interpolation functions Disorder degree Natural circular frequency Free vibration response

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ON interpolation functions FOR GENERALIZED LI COEFFICIENTS IN THE SELBERG CLASS

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INTERNATIONAL JOURNAL OF NUMBER THEORY 2011年第3期7卷 771-792页

作者： Odzak, Almasa Smajlovic, Lejla Univ Sarajevo Dept Math Fac Econ Sarajevo 71000 Bosnia & Herceg

We prove that there exists an entire complex function of order one and finite exponential type that interpolates the Li coefficients lambda(F)(n) attached to a function F in the class S-#b that contains both the Selberg class of functions and (unconditionally) the class of all automorphic L-functions attached to irreducible, cuspidal, unitary representations of GL(n)(Q). We also prove that the interpolation function is (essentially) unique, under generalized Riemann hypothesis. Furthermore, we obtain entire functions of order one and finite exponential type that interpolate both archimedean and non-archimedean contribution to lambda(F)(n) and show that those functions can be interpreted as zeta functions built, respectively, over trivial zeros and all zeros of a function F is an element of S-#b.

关键词： Generalized Li coefficients Selberg class interpolation functions

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Derivation of a BC_n Elliptic Summation Formula via the Fundamental Invariants

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CONSTRUCTIVE APPROXIMATION 2017年第1期45卷 33-46页

作者： Ito, Masahiko Noumi, Masatoshi Tokyo Denki Univ Sch Sci & Technol Future Life Tokyo 1208551 Japan Kobe Univ Dept Math Kobe Hyogo 6578501 Japan

We give an alternative proof of an elliptic summation formula of type by applying the fundamental invariants to the study of Jackson integrals associated with the summation formula.

关键词： BCn elliptic summation formula Jackson integrals Fundamental invariants interpolation functions q-Difference equations

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