In addition, it is more flexible as it can be degenerated to the first-order shear deformation plate theory (FSDT) of Reissner and Mindlin if the higher-order rotation coefficients are neglected and a shear correction factor is considered, or to the TSDT if the relevant rotation coefficients are constrained.
In this paper we proposed a method to design and numerically calculate high-order rotation invariants from Gaussian–Hermite moments.
The construction of the sets of plate equations is systematized by the introduction of recursion relations which relates higher order powers of displacement and micro-rotation terms with the lower order terms.
And, the higher order intrinsic mode corresponds to the shorter rotation angle of mode conversion.
Lagrangian linear interpolation functions are used to describe the in-plane displacements and the rotation of normals about x and y axes; Hermitian cubic interpolation functions are given for the transverse displacement, rotation about z-axis, higher order term of displacements and their first derivation.
Moreover, rotation should be very precise when higher order spatial frequency terms are required, which are particularly sensitive to azimuthal position errors.
Equipped with higher order approximation capabilities the used NURBS functions focus increasingly on rotation-free shell elements which are considered to be difficult in the traditional finite element framework.
It is important to highlight that the expanded constellation, resulting from component interleaving and ordinary constellation rotation, does not convert a low order constellation to higher order.
A hierarchy of higher order continua is presented that introduces additional degrees of freedom accounting for volume changes, rotation and straining of an underlying microstructure.
We verify by experiments the rotation invariance and show that we are capable of computing much higher order of Gaussian–Hermite invariants than of geometric invariants, which brings better discrimination power.
The rotation at the top boundary is non-zero to fulfill the balance equations and higher order traction boundary condition m y=H/2)=0.
