On Generalizations of the Minimal Complementary Energy Variational Principle in Linear Elastostatics

Jiashi Yang

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arXiv · 2409.06875

On Generalizations of the Minimal Complementary Energy Variational Principle in Linear Elastostatics

Jiashi Yang

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Abstract

It is shown that when the well-known minimal complementary energy variational principle in linear elastostatics is written in a different form with the strain tensor as an independent variable and the constitutive relation as one of the constraints, the removal of the constraints by Lagrange multipliers leads to a three-field variational principle with the displacement vector, stress field and strain field as independent variables. This three-field variational principle is without constrains and its variational functional is different from those of the existing three-field variational principles. The generalization is not unique. The procedure is mathematical and may be used in other branches of physics.

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Jiashi Yang. 2024-09-10. On Generalizations of the Minimal Complementary Energy Variational Principle in Linear Elastostatics. https://arxiv.org/abs/2409.06875

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