What Is Thin Film Analysis?

Thin film comparison is a comparison method commonly used in experimental stress analysis. Using the similarity of the elastic film with the torsion and bending problem, the unknown quantity of the torsion and bending problem is determined through the study of the film.

Thin film comparison is a comparison method commonly used in experimental stress analysis. Using the similarity of the elastic film with the torsion and bending problem, the unknown quantity of the torsion and bending problem is determined through the study of the film.

Chinese name

Thin film analogy

Foreign name

membraneanalogy

Thin film analogy

German L. Plant has contributed a lot to solid mechanics. His doctoral dissertation (1899) explored the lateral stability of narrow rectangular beams. The thin film analog method of column torsion was proposed in 1903, and was later used by AA Griffiths and GI Taylor to determine the torsional stiffness of cylinders with various complex sections. ^[1]

Thin film analogy

From the theory of elasticity ^{[2], it is} known that the transverse deflection of a uniformly stretched elastic film and the shear stress in the cross section of a torsion bar with constant cross section are described by Poisson's equation:

(1)

(2)

Its boundary conditions are:

(3)

(4)

Where w is the deflection of the film; p is the transverse force per unit area;

Is the tensile force per unit length on the film boundary; is the torsional stress function; G is the shear modulus; is the torsion angle (radian) per unit length; S _i is the boundary of the cross section of the film and the member ( i = , 2); x and y are rectangular coordinates. It can be seen that if the boundary of the film is on a horizontal plane, its shape is similar to the cross section of the torsion bar, and Cp /

= 2G ( C is proportional constant), then the deflection w ( x , y ) is proportional to the torsional stress function ( x , y ). During the test, a hole with a shape similar to the cross-section of the torsion bar is made in a flat plate, and a film (such as a rubber film, a soap film, etc.) is stretched on the hole. Flex. The contours of the film after deflection were measured (Figure 1). The following results can be obtained from the contour map: The tangential direction of the contour line at any point on the film is the direction of the shear stress at the corresponding point on the cross section of the torsion bar. The maximum slope of any point on the film (which can be calculated from the vertical and horizontal spacing of the contour lines) is proportional to the shear stress at the corresponding point on the cross section of the torsion bar. If a circular hole is opened on the same plate (such as the circular hole on the right side of Figure 1), the same film is stretched, and the same air pressure is applied, the ratio can be calibrated. The volume contained between the surface of the flexure film and the surface of the flat plate is proportional to the torque of the torsion bar. ^[3]

If the transverse force per unit area on the film is p = 0, the mechanical problem described by the Laplace equation can be simulated, that is,

(5)

(6)

In the plane stress field, = ( ₁ + ₂ ) represents the sum of principal stresses, which is proportional to the height h of the film. The film comparison is particularly suitable for determining the torsional properties of non-circular cross-section members.

Thin film analog applications

Thin film analog twist

Studying the deformation of an elastic film subjected to uniform lateral pressure can be found when certain physical quantities (such as pressure and surface tension) in the film and some physical quantities (such as torsion angle and shear per unit length) When the modulus G ) satisfies a certain relationship, the value of the physical quantity in the torsion problem can be determined by the value of the corresponding physical quantity in a film with the same cross-sectional shape as the cylinder. For example, the shear stress component at any point in the cylinder can be determined by the slope of the film in the direction perpendicular to the shear stress at the corresponding point of the film. It can be concluded from this that the direction of the combined forces of shear stress is the tangential direction of the film contour, and the maximum shear stress occurs at the point where the film contour is most dense. ^[4]

After neglecting the effect of local stress, the torsion results of the narrow rectangular section cylinders obtained by the film comparison method can be used to solve the torsion of thin-walled members with openings. If the thin film analog method is used to solve the torsion problem of thin-walled members with two or more boundaries, the inner boundary needs to be replaced by a rigid flat plate without weight, and twice the volume covered by the film is equal to the torque The relationship and the shear stress loop formula are solved simultaneously, so that the shear stress component can be obtained. The so-called shear stress loop quantity formula is that the integral of the shear stress on the contour line of the film is constant, that is,

Where A is the area enclosed by the contour lines.

The film is more curved

The bending problem of a cantilever cylinder can be compared with a film subjected to only uniform tensile force. In the comparison, the film should be tensioned on a horizontal hole with the same shape as the cross section of the cylinder. The height of the film is the stress function at the corresponding point on the cross section. Substituting the obtained value into the following formula can obtain the shear stress component: