Abstract
In this chapter we will give solutions for plates, which are loaded only on their edges. This implies that no distributed forces px and py occur, and the fourth-order bi-harmonic equation (1.23) reduces to the simple form
When a general solution has been found for u x , the solution for u y can be derived from the relation between u x and u y as given in Eq. (1.17). If we choose the first equation, the relation is (P x = P y = 0)
We will demonstrate two types of solution. In the first type, solutions for the displacements u x and u y will be tried, which are polynomials in x and y. We will see that interesting problems can be solved through this ’inverse method‘. The second type of solution is found by assuming a periodic distribution (sine or cosine) in one direction. Then in the other direction an ordinary differential equation has to be solved. This approach is suitable for deep beams or walls.
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Blaauwendraad, J. (2010). Applications of the Plate Membrane Theory. In: Plates and FEM. Solid Mechanics and Its Applications, vol 171. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3596-7_2
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DOI: https://doi.org/10.1007/978-90-481-3596-7_2
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