Results 231 to 240 of about 6,255,996 (283)
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2009
The basic equations of linear elasticity are derived in chapter 1 and are conveniently divided into three groups: the equilibrium equations, the strain-displacement relationships, and the constitutive laws, as illustrated in fig. 9.33. In chapter 9, two virtual work principles are derived.
Bauchau, Olivier, Craig, JI
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The basic equations of linear elasticity are derived in chapter 1 and are conveniently divided into three groups: the equilibrium equations, the strain-displacement relationships, and the constitutive laws, as illustrated in fig. 9.33. In chapter 9, two virtual work principles are derived.
Bauchau, Olivier, Craig, JI
openaire +3 more sources
2021
The deep energy method is an alternative to the physics-informed neural networks (PINNs). Both approaches leverage the underlying physics to reduce the amount of data required. Instead of directly using the governing differential equations, the deep energy method minimizes the potential energy of the underlying physical system. This approach lowers the
Stefan Kollmannsberger +3 more
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The deep energy method is an alternative to the physics-informed neural networks (PINNs). Both approaches leverage the underlying physics to reduce the amount of data required. Instead of directly using the governing differential equations, the deep energy method minimizes the potential energy of the underlying physical system. This approach lowers the
Stefan Kollmannsberger +3 more
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Mechanism and Machine Theory, 1975
Abstract A new procedure for constructing the solution to conservative, linear, and nonlinear initial value problems is given. Numerical results are given for a linear mechanical oscillator and a nonlinear simple pendulum. The method given does not employ or even require the formulation of differential equations, but is compared to several methods ...
K.M Ragsdell, W.J Carter
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Abstract A new procedure for constructing the solution to conservative, linear, and nonlinear initial value problems is given. Numerical results are given for a linear mechanical oscillator and a nonlinear simple pendulum. The method given does not employ or even require the formulation of differential equations, but is compared to several methods ...
K.M Ragsdell, W.J Carter
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2018
Most of semi-analytical techniques, based on Energy Balance method (EBM), are presented in this chapter and the fundamental of Energy Balance method and its modified version, based on the Galerkin and Petrov–Galerkin approaches, are discussed. The first-, second- and the third-order Hamiltonian approaches are comprehensively illustrated and the ...
Ebrahim Esmailzadeh +2 more
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Most of semi-analytical techniques, based on Energy Balance method (EBM), are presented in this chapter and the fundamental of Energy Balance method and its modified version, based on the Galerkin and Petrov–Galerkin approaches, are discussed. The first-, second- and the third-order Hamiltonian approaches are comprehensively illustrated and the ...
Ebrahim Esmailzadeh +2 more
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2020
Determination of the stability chart and transition curves of parametric differential equations are extremely important in design, optimization, and study of parametric systems. Besides several approximate methods that are capable of determining the stability chart of parametric systems, the energy-rate method is the most exact one.
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Determination of the stability chart and transition curves of parametric differential equations are extremely important in design, optimization, and study of parametric systems. Besides several approximate methods that are capable of determining the stability chart of parametric systems, the energy-rate method is the most exact one.
openaire +1 more source