In this paper, when Reynolds number is within the range of 10000 to 1000000, the horizontal component of the total pressure of flow around flat plate at high angle of attack was regarded as lift of high angle of attack, and the vertical component was regarded as drag of high angle of attack. The horizontal component of total pressure at small angle of attack was regarded as shape drag, and the total drag coefficient at small angle of attack was considered to the sum of the shape drag and frictional drag at zero angle of attack. For the two states of large and small angle of attack, the application scopes of the formulas of lift and drag coefficients were given. Final, the relations of lift and drag coefficients were obtained by eliminating all angles of attack. Research results show that lift - drag curve of small angles of attack is parabola, and the lift - drag curve of high angles of attack is circle.

The calculations of the elastic modulus and the internal stresses of the orthogonal symmetric laminated plates are very difficult, so experimental or numerical simulation methods were used generally. This paper proposed an Equivalent Strain Model, which can greatly simplify the derivation process of the analytical formulas. By the Equivalent Strain Model, the elastic modulus formula of two-layer plate was derived, and the formula shows that the elastic modulus of the laminated plate meets to the mixture rule of the cross-sectional area ratio of each its single-layer plate; Other formulas derived show that the stress within each single-layer plate is proportional to its elastic modulus and the external load stress, and is inversely proportional to the elastic modulus of the laminated plate. The formula of the average shear stress between two single-layer plates also was derived. Recursive method can be used for multilayer plate calculations.

To study the impact of an airfoil shape on performance, a curve expression of airfoil shape was proposed, the analytical formula for the pressure distribution of flow around the airfoil was derived, and the pressure distribution view around airfoil with azimuth as the independent variable was put forward, which can clearly express the details of the pressure distribution curve on airfoil leading edge. Used both the pressure distribution integration method and Blasius theorem, the lift coefficient calculation formulas of ideal fluid flow around the airfoil were derived respectively, and the same results were obtained. Studies have shown that the shape of an airfoil can be expressed by a function, and various types of shapes can be easily obtained by adjusting the constant value in the expression; The pressure distribution and lift coefficient can be calculated by analytical method; For function airfoil, lift coefficient formula could be derived by two methods, and could be verified with each other. The one-to-one relationship exists between the constant values in the airfoil function, airfoil shapes and airfoil performances, and the relationship expression was given in this paper.

Settlement and inclination of gravity foundation are calculated and analyzed using transfer matrix method. The influences of vertical load, overturning moment, foundation width b and deformation modulus of subgrade soil E on the settlement and inclination of foundation are analyzed. Calculation shows that increasing both the width of foundation b and deformation modulus of subgrade soil E can improve the anti-overturning performance of foundation, and reducing the foundation width and increasing the deformation modulus of subgrade soil can reduce the subgrade settlement. This method can effectively calculate the settlement and inclination of gravity foundation.

To facilitate the airfoil design, this paper studied the methods of constructing analytic functions to generate airfoil profiles. By Taylor series, Joukowsky airfoil function was simplified to a simple expression, and its coefficients and exponents were redefined as general constants. A series of simple airfoils can be generated by changing the assignment of the constants in the expression. Further, many complex airfoil images could be obtained by recombining upper profile functions and lower profile functions of other airfoils or by adding a number of thickness functions in the expression. Studies have shown that the structure of the expression is simple and the geometric meaning of the parameters in it is clear, which is suited for expressing airfoil shape; according to the parameter assignment rule summarized in this paper, the desired airfoil shape can be easily generated.