Thermal buckling analysis of variable angle tow plates

Abstract

Many industrial vehicles, especially aviation sector, are exposed to thermal loads due to high temperature changes. In these structures, which are designed with the principle of lightness and strength, composite materials are frequently preferred due to their outstanding mechanical properties. Composite materials are usually formed into plates for ease of production and intended use. These plates can face many loading and failure. For instance, composite plates may show unstable behavior and buckle under thermal loads. Scientists and engineers who want to keep composite structures away from this failure have started to use variable angle composites in this field, based on the parameters affecting buckling. Here the idea of angle propagation is dominant, which depends on the orientation angle of the edge and center part of the plate, rather than having the same angle in the same layer throughout the plate. Thus, the material will be used effectively and maximum buckling strength will be provided with an optimized angle orientation and minimum material usage. Many tests and calculations have been made for this. However, for a specific design of a variable angle composite, material design, calculations are not fast enough. One of the main reasons for this is that package programs using the finite element method are only suitable for modeling straight-angle composites and are not suitable for performing calculations for variable-angle composites. From this point of view, it is focused on creating a code in which the necessary calculations will be made without the need to use package programs. This study focuses on a code that can calculate the critical buckling temperature of variable-angle composite plates. This code requires geometric dimensions, mechanical and thermal properties of the material, boundary conditions, and the desired number of elements as input. After the inputs are provided, the code; using the finite element theory, the desired number of nodes and elements is formed to include shape functions. The code associates the geometric properties of these elements with the material properties and makes them suitable for calculations. It determines the different orientations in the in-plane position with the help of the function containing the edge and center angles of the plate. In this step, based on the Classical Lamination Theory, the material matrices, transformation matrices, etc. are calculated for A, B, D stiffness matrices and thermal loads. After calculating the A, B, D matrices of the composite, the strain-displacement matrices per unit length are generated based on the finite element method. As a result of processing these matrices with the appropriate A, B, D matrices, the stiffness matrix of the plate is obtained. The calculated stiffness matrix is one of the two basic matrices that decides whether the plate will buckle or not. A similar procedure was followed for the geometric stiffness matrix, which is another stiffness matrix required for the buckling analysis. In the geometric stiffness matrix, unlike the material stiffness matrix, the initial stress matrix is used instead of the material matrix. Thus, the effects of stress were tried to be added to the structure. The eigen value calculation is required for the estimation of the buckling failure that occurs as a result of the relations of the two stiffness matrices formed with each other. This factor is obtained by the code as a result of the necessary matrix operations, taking into account the boundary conditions. The eigenvalue is calculated as much as the unconstrained total degrees of freedom. It is generally sufficient to observe the 10 most critical of them. Since a buckling analysis is performed under thermal load, the output of this analysis will be the critical buckling temperature. This value indicates how far the structure is from buckling. By considering this value, the people responsible for the design can determine what the working environmental conditions should be by ensuring that the structure stays away from the unsafe region. This code was tried to be verified with some studies in the literature (Duran, Babu), analytical formulas, and finite element model created using MSC Patran application. It was built in order from the basics to the details. The results of the validation analyses taken with low error rates in different categories are presented in tabular form. Thus, the code has become suitable for use in thermal buckling analysis of variable angle composites. Thus, the code has reached the capability to determine whether the structure is safe or under which conditions it will be safe in designs that are created with variable angle composites and need to control buckling under temperature. It has been seen with the help of the code that the variable angle composite modeled using an example material, geometry and orientation reaches temperatures higher than the highest critical buckling temperature of a straight composite with the same properties. Thus, calculating the buckling factors of variable-angle composites, which makes straight-angle composites more effective in buckling, which is the purpose of preparing the code, has been achieved. Some studies that can be added to the code for future studies are also specified in the code.