Theoretical Base for Determining the Modulus of Elasticity of Thin Plate Compressed by Concentrated Force

Abstract

An analytical solution to the plane problem in elasticity theory is presented for the case of a concentrated transverse force acting on a thin, sufficiently wide plate. A functional relationship is obtained which allow to determine the displacements of points on the plate located along the line of force application depending on the distance from the point of force application. Using an example, by comparing analytical and numerical calculations of the displacement of a specific point, it is shown that the formula derived from the established relationship provides quite accurate results. The proposed formula is recommended for determining the first-order elastic modulus based on measured force and displacement parameters.

Keywords

• thin plate
• compression
• stress
• deformation
• displacement
• boundary conditions
• modulus of elasticity
• bone tissue
• gunshot fracture
• biomechanics