The symplectic approach for analytical solution of micropolar plane stress problem. (1st March 2023) - Wu, Qiong; Gao, Qiang
Highlights: The symplectic method is adopted to solve the micropolar plane stress problems. Analytical solutions of strip domain with different boundary conditions are obtained. The solutions are expressed by the eigensolutions of Hamiltonian operator matrix. Size effect is analyzed by the relation between eigenvalues and material constants. Abstract: The symplectic method is adopted to derive analytical solution of the plane stress problem in the framework of the micropolar elasticity. The general micropolar plane stress problem is transformed into three types of problems with homogeneous boundary conditions at two opposite edges. The fundamental equations are converted into canonical Hamiltonian equations using the Legendre transformation. The eigensolutions of the Hamiltonian operator matrix are obtained for three types of homogeneous boundary conditions. The analytical solution for the micropolar plane stress problem is expressed as an eigensolution expansion. The size effect is analyzed based on the relationship between the eigenvalues and micropolar material constants. The numerical results obtained by the finite element method (FEM) and ABAQUS demonstrate the validity of the proposed method for different boundary conditions and confirm its ability to accurately capture the size effect.