Q1: The vertical displacement of a cable, suspended between two horizontal fixed points is governed by:...

Transcribed Image Text:

Q1: The vertical displacement of a cable, suspended between two horizontal fixed points is governed by: d dw(x) To dx dx x)0 (1) where w(x) is the vertical displacement, To is the tension force and q(x) is the vertical load. This physical problem can be solved using the finite element method. Assuming, that the cable is stationary, derive the element stiffness matrix using the Galerkin method. Use a linear finite element. [3 marks] Q2: Consider a bar shown in figure Q2 with an axial load P = 50 kN applied as shown. The bar is split into 2 finite elements. Element 1 is made of an aluminium alloy with E 20 x 103 Nmm2 with a cross sectional area, A 800mm2. Element 2 is made of steel with E 200 x 103 Nmm2 with a cross sectional area, A 600 mm2. Nodes 1 and 3 are fixed. (a) Determine the nodal displacements. (b) Determine the stress in each material. (c) Determine the reaction forces. (d) Check your answers using FEM1D program. 1 2 P 1 2 600mm 400mm Figure Q2: A tapered bar with a point load, geometry and finite element mesh. [2 marks] Q1: The vertical displacement of a cable, suspended between two horizontal fixed points is governed by: d dw(x) To dx dx x)0 (1) where w(x) is the vertical displacement, To is the tension force and q(x) is the vertical load. This physical problem can be solved using the finite element method. Assuming, that the cable is stationary, derive the element stiffness matrix using the Galerkin method. Use a linear finite element. [3 marks] Q2: Consider a bar shown in figure Q2 with an axial load P = 50 kN applied as shown. The bar is split into 2 finite elements. Element 1 is made of an aluminium alloy with E 20 x 103 Nmm2 with a cross sectional area, A 800mm2. Element 2 is made of steel with E 200 x 103 Nmm2 with a cross sectional area, A 600 mm2. Nodes 1 and 3 are fixed. (a) Determine the nodal displacements. (b) Determine the stress in each material. (c) Determine the reaction forces. (d) Check your answers using FEM1D program. 1 2 P 1 2 600mm 400mm Figure Q2: A tapered bar with a point load, geometry and finite element mesh. [2 marks]