Study of thin plate bending using the method of holographic moiré

The development of the technique of applying high-frequency metallized working images to products made of any materials led to the emergence of the holographic moiré method. This method is based on recording holograms in counter beams and is traditionally used to study the displacements in the working raster plane. This paper shows that if, when holograms are recorded, the registering medium is placed at a considerable distance from the working screen surface, then the recorded optical information makes it possible to determine the inclination angles of the surface under study. We present the results of a study of bending of a thin, round, rigidly clamped plate. The plate was subjected to hydrostatic bending. A good agreement between the experimental data and the theoretical solution is obtained.

R-Function and variation method for bending problem of clamped thin plate with complex shape

Solving ordinary thin plate bending problem in engineering, only a few analytical solutions with simple boundary shapes have been proposed. When using numerical methods (e.g. the variational method) to solve the problem, the trial functions can be found only it exhibits a simple boundary shape. The R-functions can be applied to solve the problem with complex boundary shapes. In the paper, the R-function theory is combined with the variational method to study the thin plate bending problem with the complex boundary shape. The paper employs the R-function theory to express the complex area as the implicit function, so it is easily to build the trial function of the complex shape thin plate, which satisfies with the complex boundary conditions. The variational principle and the R-function theory are introduced, and the variational equation of thin plate bending problem is derived. The feasibility and correctness of this method are verified by five numerical examples of rectangular, I-shaped, T-shaped, U-shaped, and L-shaped thin plates, and the results of this method are compared with that of other literatures and ANSYS finite element method (FEM). The results of the method show a good agreement with the calculation results of literatures and FEM.

Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration

As it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini’s element (ACM element), are often recommended for practical usage. However, the convergence, good numerical accuracy, and high computing efficiency of ACM element with irregular physical boundaries cannot be achieved using either the finite element method (FEM) or the numerical manifold method (NMM). The mixed-order NMM with background cells for integration was developed to analyze the bending of nonconforming thin plates with irregular physical boundaries. Regular meshes were selected to improve the convergence performance; background cells were used to improve the integration accuracy without increasing the degrees of freedom, retaining the efficiency as well; the mixed-order local displacement function was taken to improve the interpolation accuracy. With the penalized formulation fitted to the NMM for Kirchhoff’s thin plate bending, a new scheme was proposed to deal with irregular domain boundaries. Based on the present computational framework, comparisons with other studies were performed by taking several typical examples. The results indicated that the solutions achieved with the proposed NMM rapidly converged to the analytical solutions and their accuracy was vastly superior to that achieved with the FEM and the traditional NMM.

The Transverse Shear Effect of a New Strain Based Sector Finite Elements for Plate Bending Problems

In this paper, we present the transverse shear effect on the plate bending. The element used is a sector finite element called SBSP (Strain Based Sector Plate-Kirchhoff Theory-), it used for the numerical analysis of circular thin plate bending., and it based on the strain approach. This element has four nodes and three degrees of freedom per node. Through the numerical applications with different loading cases and boundary conditions; This makes the present element robust, better suitable for computations.

Mechanical Characteristics of Origami Mechanism Based on Thin Plate Bending Theory

This paper introduces a method for calculating the deformation displacement of the origami mechanism. The bearing capacity of each face can be analyzed by the relationship between the stress and displacement, which can provide a reference for the origami design. The Miura origami mechanism unit is considered. First, the folding angle of each crease is solved based on the geometric characteristics. The deforming form of the creases is then analyzed, and the bending moment acting on the paper surface is solved. Based on the geometric characteristics and stress forms, the paper surface is modeled as a sheet. Based on the bending theory of a thin plate with small deflection, the complex external load forms are decomposed by Levy's method and the superposition principle, and the expression of the deflection curve during the folding process is obtained. According to the stress and bending moment equations, the relationship between the bending moment and displacement is obtained. Finally, through an application example, the maximum deflection of the paper surface is calculated by matlab, and the deflection diagram of the deformed paper surface is drawn, which verifies the expression of the deflection curve.