Principles of Minimum Potential Action and Stationary Complementary Action With Dual and Triple Mixed Variables for Linear Elastodynamics of Finite Displacement Theory and the Application

FU Bao-lian

doi:10.21656/1000-0887.380005

Volume 38 Issue 12

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FU Bao-lian. Principles of Minimum Potential Action and Stationary Complementary Action With Dual and Triple Mixed Variables for Linear Elastodynamics of Finite Displacement Theory and the Application[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1359-1376. doi: 10.21656/1000-0887.380005

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Principles of Minimum Potential Action and Stationary Complementary Action With Dual and Triple Mixed Variables for Linear Elastodynamics of Finite Displacement Theory and the Application

doi: 10.21656/1000-0887.380005

FU Bao-lian

College of Architectural Engineering and Mechanics, Yanshan University,Qinhuangdao, Hebei 066004, P.R.China

Received Date: 2017-01-05
Rev Recd Date: 2017-05-13
Publish Date: 2017-12-15

Abstract

Abstract

2 new concepts, potential action and complementary action, were first introduced into the variational principles for linear elastodynamics. On the basis of the concept of potential action, the principle of minimum action (Hamilton’s principle) was renamed to the principle of minimum potential action. In terms of the concept of complementary action, the principle of stationary complementary action was proposed for the first time. Next, the principles of minimum potential action and stationary complementary action with dual mixed variables of displacement and stress were derived in view of the boundary condition changes by means of the reciprocal theorem. And then, through the application of the relations between the strain energy density and the complementary energy density to the above 2 principles with dual mixed variables, the principles of potential action and complementary action with triple mixed variables of displacement, stress and strain were derived. Finally, the generalized principles of potential action and complementary action were given with the Lagrange multiplier method, in the meantime, the principle of minimum potential action with dual mixed variables of large deflection beams was applied to the calculation of a bending cantilever beam under forced vibration.

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References(20)

References

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