A Generalized Unit System for Concise Electromagnetic Formulation and Accurate Numerical Solutions

Vu‐Quoc, L.; Srinivas, V.; Zhai, Yuhu

doi:10.1006/jcph.2002.7116

Cited by 4 publications

(8 citation statements)

References 13 publications

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“…The consistent tangents are which complete the FE formulation. According to Vu‐Quoc et al 27, the numerical behavior of a fully coupled electro‐mechanical formulation can be improved by using a re‐normalized system of units.…”

Section: Fe Implementationmentioning

confidence: 99%

A variational, finite‐deformation constitutive model for piezoelectric materials

Mota

Zimmerman

2011

Numerical Meth Engineering

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SUMMARYWe present a constitutive model for piezoelectric materials. The model is fully variational and supports finite kinematics. The postulated free energy depends on the deformation mapping and an electric vector potential, from which the strain and the electric displacement are derived, respectively. The divergence-free condition of the electric vector potential is enforced by means of a penalty method, which leads to a positive definite tangent for the system of equations that represent the problem. The performance of the formulation is demonstrated by several examples. Published in

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Section: Fe Implementationmentioning

confidence: 99%

A variational, finite‐deformation constitutive model for piezoelectric materials

Mota

Zimmerman

2011

Numerical Meth Engineering

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“…Note that the two equations in (26) are identical to the two equations in (27) since the weighting functions w r and w i can be arbitrarily selected. Therefore, treating the weak form of the real part and of the imaginary part separately is equivalent to using the combined complex notation, but with the advantage of being simpler and computationally more e cient.…”

Section: Remark 31mentioning

confidence: 99%

“…Algorithm 6.1 is used to analyse capacitors below 10 5 Hz, and Algorithm 6.2 is used to analyze capacitors above 10 5 Hz. For Algorithm 6.2 a multiple scale technique [26] is used to improve accuracy. In the solution presented below, the Coulomb gauge is imposed via a penalty method and one-point reduced integration.…”

Section: Time-harmonic Analysis Of Multi-layer Ceramic Capacitorsmentioning

confidence: 99%

“…These two algorithms in conjunction with a multiple-scale technique [26] are implemented in the ÿnite element codes FEAP and MODULEF.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 6, we introduce two algorithms to analyse the behaviour of the capacitor with the change in frequency. These two algorithms in conjunction with a multiple-scale technique [26] are implemented in the ÿnite element codes FEAP and MODULEF. * * Static and timeharmonic solutions for Maxwell equations are implemented.…”

Section: Introductionmentioning

confidence: 99%

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Finite element analysis of advanced multilayer capacitors

Vu‐Quoc

Srinivas

Zhai

2003

Numerical Meth Engineering

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SUMMARYWe establish a systematic methodology to design and analyse electromagnetic components such as advanced multilayer ceramic capacitors (MLCCs) using the ÿnite element (FE) method. We employ a coupled formulation to compute the interaction between the electric and magnetic ÿelds. Unlike a linear distribution of current assumed in the circuit model, an accurate electrostatic solution to model the entire advanced MLCCs (4 × 4 × 27 = 432 cells) is presented. The FE solution is used to compute the lumped parameters for a range of frequencies. These lumped parameters are then used to compute the parasitic elements of the MLCCs. We introduce two algorithms to e ciently analyse the behaviour of a capacitor with changing frequency. The lower frequency (much below the selfresonant frequency of the capacitor) algorithm separates the e ect of the electric and magnetic ÿelds and reduces the computational e ort required to solve the FE problem, whereas, the high-frequency algorithm couples the e ect between the electric and the magnetic ÿelds. We use these algorithms in conjunction with a new multiple scale technique to e ectively determine the small values of R, L and C in MLCCs. The formulation, the implementation, and the numerical results demonstrate the e cacy of the present FE formulation and establish a systematic methodology to design and analyse advanced electromagnetic components.

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Analysis of power magnetic components with nonlinear static hysteresis: finite-element formulation

Zhai

Vu‐Quoc

2005

IEEE Trans. Magn.

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A Generalized Unit System for Concise Electromagnetic Formulation and Accurate Numerical Solutions

Cited by 4 publications

References 13 publications

A variational, finite‐deformation constitutive model for piezoelectric materials

A variational, finite‐deformation constitutive model for piezoelectric materials

Finite element analysis of advanced multilayer capacitors

Analysis of power magnetic components with nonlinear static hysteresis: finite-element formulation

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