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Convolved action principles for couple stress elastodynamics
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DOI：10.1016/j.ijmecsci.2023.108263.png)
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摘要
En 中文
A novel set of variational principles and integral theorems is developed for consistent couple stress elastody-namics, including the principle of virtual convolved action, the principle of stationary convolved action, the theorem of dynamic reciprocity and the integral representation theorem. Both time-domain and Laplace-domain versions are presented. Most notably, all of these are based on the concept of convolved action, involving temporal convolutions, and are applicable to the most general case of bi-anisotropic couple stress materials. Furthermore, the principle of virtual convolved action extends beyond elastodynamics to viscoelastic and plastic material response. In addition, the two-dimensional infinite space fundamental solutions and kernel functions are derived in the Laplace-domain and used to formulate a new boundary element method (BEM) for transient response, which also originates from a convolved action. The resulting BEM is applied to four prototype examples to demonstrate the validity and robustness of the method, and to explore interesting behavior of consistent couple stress elastodynamics in the isotropic case. Although the focus here is solely on couple stress elastody-namics, the convolved action framework extends to a broad range of time-dependent problems, including those of a multiphysical nature.
Keyword:
Size-dependent elastodynamics
Skew-symmetric couple-stress
Convolved action and virtual action
Dynamic reciprocal and integral representation
theorems
Fundamental solutions
Micromechanics and nanomechanics
期刊
IF:
9.4
论文数:
1.0W
被引数:
4.5W
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A three-dimensional weak formulation for stress, deformation, and free vibration analyses of functionally graded microscale plates based on the consistent couple stress theory.png)
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