Moreover, the transverse radiation force cross-section field changes with the sphere׳s size factor ka (where k is the wavenumber and a is the sphere radius).
The shape optimization mathematical model of prestressed cable-truss structures is founded, and its design variables includes three kinds of design variables: cable pretension force, cross-section size, and element-node coordinates.
The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections.
Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization.
Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively.
It shows that: if R-wave propagates along the axis of a tunnel, the longitudinal axial force, bending moment and shear force on a cross section can reach their respective maxima.
If external axial forces are not acting on a cantilevered beam, the resultant axial force at any cross section along the beam is equal to zero.
Open image in new window Fig. 7 Theoretical strain and Stress distribution and internal forces on the cross section.
A model was established to predict normal forces of constant cross section (CCS) disc cutters in the rock cutting process by using fuzzy logic method.
According to the plane section assumption, OpenSees automatically calculates the strain of each fiber and ensure forces of the cross section keeping balance through iterative treatment.
The blade element theory is based on the equation of lift and drag forces on the cross section of a blade.
