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Solution of the exact differential equation of deflection curve
Šikl, František ; Fuis, Vladimír (referee) ; Vaverka, Jiří (advisor)
This bachelor thesis deals with the deformation of a beam loaded with a basic bend using the differential equation of the deflection curve. The work is divided into four parts, where in the first part the general form of the differential equation of the deflection curve, which is based on simple geometry and mathematical approximations, is derived. In the second part, we will describe the basic methods of solving the differential equation of the deflection curve for large deformations for simple cases, where we must use the nonlinear form of the already mentioned equation. However, we will also mention methods that can be used for specific cases. In the third part, two numerical methods, which can be used to solve large deformations of beams, are being programmed. The last part describes the difference between the linear equation of the deflection curve, which is simplified and taught commonly, and the nonlinear differential equation of the second order. The fundamental task of the work is a comparison of commonly used methods to determine the deformation of the beam and to determine the degree of load, when it is possible to use a simplified differential equation of the deflection curve, and when not. However, it is important to mention that the numerical solution cannot always be used, so the example will be embedded in a simple case.
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Solution of the exact differential equation of deflection curve
Šikl, František ; Fuis, Vladimír (referee) ; Vaverka, Jiří (advisor)
This bachelor thesis deals with the deformation of a beam loaded with a basic bend using the differential equation of the deflection curve. The work is divided into four parts, where in the first part the general form of the differential equation of the deflection curve, which is based on simple geometry and mathematical approximations, is derived. In the second part, we will describe the basic methods of solving the differential equation of the deflection curve for large deformations for simple cases, where we must use the nonlinear form of the already mentioned equation. However, we will also mention methods that can be used for specific cases. In the third part, two numerical methods, which can be used to solve large deformations of beams, are being programmed. The last part describes the difference between the linear equation of the deflection curve, which is simplified and taught commonly, and the nonlinear differential equation of the second order. The fundamental task of the work is a comparison of commonly used methods to determine the deformation of the beam and to determine the degree of load, when it is possible to use a simplified differential equation of the deflection curve, and when not. However, it is important to mention that the numerical solution cannot always be used, so the example will be embedded in a simple case.
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