A Finite Difference Solution of a Simply Supported Beam of Orthotropic Composite Materials Using Displacement Potential Formulation

Table 1

(a) Boundary conditions of different boundary segments of the simply supported beam as observed in Figure 1. (b) Boundary conditions of corner points of the simply supported beam problem as observed in Figure 1.

(a)

Boundary segment	Given boundary conditions	Correspondence between mesh points and given boundary conditions
		Mesh point on the physical boundary conditions	Meshpointontheimaginaryboundaryconditions
𝐴𝐵	𝜎𝑛,𝜎𝑡	𝜎𝑛=0	𝜎𝑡=0
𝐵𝐶	𝑢𝑛, 𝜎𝑛,𝜎𝑡	At point 𝐸 and 𝐹, 𝑢𝑛=0; Except point 𝐸 and 𝐹, 𝜎𝑛=0	𝜎𝑡=0
𝐶𝐷	𝜎𝑛,𝜎𝑡	𝜎𝑛=0	𝜎𝑡=0
𝐷𝐴	𝜎𝑛,𝜎𝑡	𝜎𝑛=−𝜎^0𝑦𝑦	𝜎𝑡=0

(b)

Corner points	Given boundary conditions	Used boundary conditions	Correspondence between mesh points and given boundary conditions
			Mesh point on the physical boundary conditions	Mesh point on the imaginary boundary conditions
𝐴	𝜎𝑛,𝜎𝑡,𝜎𝑛,𝜎𝑡	𝜎𝑛,𝜎𝑡	𝜎𝑛=−𝜎^0𝑦𝑦	𝜎𝑡=0
𝐵	𝜎𝑛,𝜎𝑡,𝜎𝑛,𝜎𝑡	𝜎𝑛,𝜎𝑡	𝜎𝑛=0	𝜎𝑡=0
𝐶	𝜎𝑛,𝜎𝑡,𝜎𝑛,𝜎𝑡	𝜎𝑛,𝜎𝑡	𝜎𝑛=0	𝜎𝑡=0
𝐷	𝜎𝑛,𝜎𝑡,𝜎𝑛,𝜎𝑡	𝜎𝑛,𝜎𝑡	𝜎𝑛=−𝜎^0𝑦𝑦	𝜎𝑡=0