Investigation of panel deformation because of impact loading in aerospace structures

Abstract

Beams and plates have been widely used in various engineering problems for many years. Isotropic materials such as aluminum, steel, and composite materials such as glass and carbon are widely used in beams and plates. Composite materials have been used in the aviation industry for a long time. With the widespread use of electric vehicles in the automotive sector, lightening projects have started to increase and studies are being carried out on the adaptation of lighter composite materials, especially instead of steel materials. Beams and plates are used in models such as bumper beams, vehicle door support beams, and hood-door plates in the automotive industry. In aviation, it is used in models such as wings and airframes. Especially in aviation, many dynamic impact problems such as bird strikes or FOD cause serious damage to the structure. This thesis investigated the impact resistance of beams and plates with static and dynamic loading conditions. The data obtained from the finite element method programs and the literature were compared with the theoretical results. Both linear beam theory and nonlinear beam theory were used in the impact analysis of beams, and linear plate theory was used in the analysis of plates. Transferring the solution algorithm of these theories to the MATLAB program aims to obtain results with low deviation in a short time. Since the modal solution of a simply supported beam or plate can be expressed as a sine or an infinite sum of sines, it can be applied to static or dynamic load cases. In this study, only simple support boundary conditions are considered, but it is possible to adapt the equations for different boundary conditions. Beams are modeled as 1-dimensional elements and plates as 2-dimensional elements. Beam ends are fixed except for the x-axis translation and y-axis rotation. In addition to the beam, the plates are also free in the y-axis translation. When the large deflection solutions of the beams are examined, it is known that it gives more acceptable results for a thin beam. Especially when the velocity or kinetic energy increases in the dynamic model, a large deflection theory is needed. Linear theory gives sufficient results for low-impact speeds or low-load situations. In the linear beam theory, the beam's movability is accepted as its length does not change depending on the deflection. Thus, the axial load along the length of the beam is neglected. Plates can be considered as a 2D model of beams. Equations are in a similar format and double sinus is used for plates. For this reason, only linear plate theory was used since the behavior of plates in 2 axes is investigated. The results obtained with the linear plate theory give satisfactory results for low-speed impacts or low forces. When there are higher displacement conditions, the stress values are higher because it gives higher deflection. Theories are studied on static and dynamic impact models. A static load acting on a very small part of the beam or plate can be considered a simplified impact model. Models have been established for different load conditions with both isotropic and orthotropic materials. Material properties are taken from studies in the literature. In addition, theoretical and numerical results are obtained with a single load, that is, a concentrated load, in order to simplify the impact model of a small projectile. While transferring the orthotropic material to the theory, the CLT is used. This widely used theory determines the characteristic of material with different orientations. Since deflection and stress occur here due to bending forces, lay-up gets important in lamination. Which layer is on the outer surface or the inner surface changes the strength of the structure. When calculating stiffness for beam and plate, a derived term for orthotropic material is used. Damage to the structure can be determined when it exceeds a specified stress limit. For this reason, stress calculation is included in the study. When calculating the tension in composite materials, is done separately for each layer. For the FEM, Abaqus-Implicit was used for static solutions and Hyperworks-Radioss was used for dynamic solutions. According to the results obtained with the FEM, it does not matter whether the solution is linear or not in small deflections. As the deflection increases, the linear solution starts to deviate. Since it is studied on simply supported beams and plates, U1 and UR2 in beams and UR1 and UR2 in plates are free in the edge boundary condition. C3D8R and SC8R elements were used for solid elements in the Abaqus program. C3D8R is suitable for the isotropic material model, and SC8R is suitable for the orthotropic material model. Element type SC4R was used for shell elements. This element type is compatible with two types of material models. Pressure loads were entered for the loading condition as they are suitable for the distributed load. In addition, a concentrated load section was used for single load application. In the Hyperworks-Radioss program, the HEXA8N element type is used for solid elements and the SHELL4N element type is selected for shell elements. Radioss explicit solver is widely used for dynamic problems. Impactor modeling with the rigid wall is possible for different mass and velocity conditions. Here, the rigid wall was found to be appropriate, since it is unimportant whether the striking object is damaged or not. The spherical type rigid wall is preferred because it is suitable for point impact. For the explicit solution, the element size is modeled with small element dimensions since it affects the time step of the solution. This situation highlights the advantage of calculating on MATLAB. Especially for high-speed impact models, the element type must be chosen very small, causing the solution time to be very long. Solutions with the FEM take approximately 1 to 10 minutes. The same solution is completed in 1 to 15 seconds in the MATLAB program. All the obtained results were compared and a correlation was tried to be established for the single load case. Here, a coefficient definition was made using the momentum equation. These coefficient calculations were repeated for different cases. Stress values were compared with the data obtained from the finite element method using the deflection values obtained from the theories. Usually the first three terms give sufficient results for the solution of the theory. When the deflection and the resulting stress results are compared, the difference is close to 1% in accordance with the assumptions of the theory. In cases where linearity is impaired by taking the results obtained from the finite element method as a reference, the difference between the results exceeds 50%.