The Experts below are selected from a list of 63 Experts worldwide ranked by ideXlab platform
Anton Tkachuk - One of the best experts on this subject based on the ideXlab platform.
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direct and sparse construction of consistent inverse mass matrices general variational formulation and application to selective mass scaling
International Journal for Numerical Methods in Engineering, 2015Co-Authors: Anton Tkachuk, Manfred BischoffAbstract:Summary Classical explicit finite element formulations rely on lumped mass matrices. A diagonalized mass matrix enables a trivial computation of the acceleration vector from the force vector. Recently, non-diagonal mass matrices for explicit finite element analysis (FEA) have received attention due to the selective mass scaling (SMS) technique. SMS allows larger time step sizes without substantial loss of accuracy. However, an expensive solution for accelerations is required at each time step. In the present study, this problem is solved by directly constructing the inverse mass matrix. First, a consistent and sparse inverse mass matrix is built from the modified Hamiltons Principle with independent displacement and momentum variables. Usage of biorthogonal bases for momentum allows elimination of momentum unknowns without matrix inversions and directly yields the inverse mass matrix denoted here as reciprocal mass matrix (RMM). Secondly, a variational mass scaling technique is applied to the RMM. It is based on the penalized Hamiltons Principle with an additional velocity variable and a free parameter. Using element-wise bases for velocity and a local elimination yields variationally scaled RMM. Thirdly, examples illustrating the efficiency of the proposed method for simplex elements are presented and discussed. Copyright © 2014 John Wiley & Sons, Ltd.
O Polit - One of the best experts on this subject based on the ideXlab platform.
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a nonlocal higher order model including thickness stretching effect for bending and buckling of curved nanobeams
Applied Mathematical Modelling, 2017Co-Authors: M Ganapathi, O PolitAbstract:Abstract An analytical approach for static bending and buckling analyses of curved nanobeams using the differential constitutive law, consequent to Eringen’s strain-driven integral model coupled with a higher-order shear deformation accounting for through thickness stretching is presented. The formulation is general in the sense that it can be deduced to examine the influence of different structural theories, for static and dynamic analyses of curved nanobeams. The governing equations derived using Hamiltons Principle are solved in conjunction with Naviers solutions. The formulation is validated considering problems for which solutions are available. A comparative study is made here by various theories obtained through the formulation. The effects various structural parameters such as thickness ratio, beam length, rise of the curved beam, and nonlocal scale parameter are brought out on bending and stability characteristics of curved nanobeams.
Manfred Bischoff - One of the best experts on this subject based on the ideXlab platform.
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direct and sparse construction of consistent inverse mass matrices general variational formulation and application to selective mass scaling
International Journal for Numerical Methods in Engineering, 2015Co-Authors: Anton Tkachuk, Manfred BischoffAbstract:Summary Classical explicit finite element formulations rely on lumped mass matrices. A diagonalized mass matrix enables a trivial computation of the acceleration vector from the force vector. Recently, non-diagonal mass matrices for explicit finite element analysis (FEA) have received attention due to the selective mass scaling (SMS) technique. SMS allows larger time step sizes without substantial loss of accuracy. However, an expensive solution for accelerations is required at each time step. In the present study, this problem is solved by directly constructing the inverse mass matrix. First, a consistent and sparse inverse mass matrix is built from the modified Hamiltons Principle with independent displacement and momentum variables. Usage of biorthogonal bases for momentum allows elimination of momentum unknowns without matrix inversions and directly yields the inverse mass matrix denoted here as reciprocal mass matrix (RMM). Secondly, a variational mass scaling technique is applied to the RMM. It is based on the penalized Hamiltons Principle with an additional velocity variable and a free parameter. Using element-wise bases for velocity and a local elimination yields variationally scaled RMM. Thirdly, examples illustrating the efficiency of the proposed method for simplex elements are presented and discussed. Copyright © 2014 John Wiley & Sons, Ltd.
M Ganapathi - One of the best experts on this subject based on the ideXlab platform.
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a nonlocal higher order model including thickness stretching effect for bending and buckling of curved nanobeams
Applied Mathematical Modelling, 2017Co-Authors: M Ganapathi, O PolitAbstract:Abstract An analytical approach for static bending and buckling analyses of curved nanobeams using the differential constitutive law, consequent to Eringen’s strain-driven integral model coupled with a higher-order shear deformation accounting for through thickness stretching is presented. The formulation is general in the sense that it can be deduced to examine the influence of different structural theories, for static and dynamic analyses of curved nanobeams. The governing equations derived using Hamiltons Principle are solved in conjunction with Naviers solutions. The formulation is validated considering problems for which solutions are available. A comparative study is made here by various theories obtained through the formulation. The effects various structural parameters such as thickness ratio, beam length, rise of the curved beam, and nonlocal scale parameter are brought out on bending and stability characteristics of curved nanobeams.
Muhammad R. Hajj - One of the best experts on this subject based on the ideXlab platform.
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Broadband and high-efficient L-shaped piezoelectric energy harvester based on internal resonance
International Journal of Mechanical Sciences, 2019Co-Authors: Xiaochun Nie, Ting Tan, Zhimiao Yan, Zhitao Yan, Muhammad R. HajjAbstract:Abstract We exploit a 1:2 internal resonance in an L-shaped beam-mass structure for broadband and high-efficient energy harvesting. The geometric nonlinearities of the structure and piezoelectric materials are introduced to establish the electromechanical-coupled distributed parameter model using the extended Hamiltons Principle and Gauss law. The analytical modal shapes of the structure are derived as well. The proposed model of the energy harvester is validated with finite element simulations and experiments. Periodic, quasi-periodic and chaotic motions are observed. The tip displacement of the system is mainly determined by the first mode while the harvested power of the system is primarily derived from the second mode for internal resonances of the first and second modes. By exploiting these resonances, the harvested power is significantly improved through the low-frequency excitation exciting high-frequency vibration. The larger harvested power and smaller tip displacement are also obtained with the load resistances corresponding to the maximum global damping. Increasing the external excitation amplitude causes an increase in the frequency bandwidth over which energy can be harvested. Compared to the linear system, the L-shaped energy harvester with 1:2 internal resonance can harvest power more efficiently over a wider frequency bandwidth with reduced vibration displacement. The maximum improvement of energy harvesting efficiency and bandwidth are 215% and 405% respectively.
