The element may interconnect in a 2-D or 3-D configuration in space. The element is mechanically equivalent to a spring, since it has no stiffness against applied loads except those acting along the axis of the member. However, unlike a spring element, a element can be oriented in any direction in a plane, and the same element is capable of tension as well as compression. Fig: 2 A Truss Element 1.3 Stress Strain relation: – As stated earlier, all deflections in FEA are evaluated at the nodes. The stress and strain in an element is calculated by interpolation of deflection values shared by nodes of the element. Since the deflection equation of the element is clearly defined, calculation of stress and strain is rather simple matter. When a load F is applied on a truss member, the strain at a point is found by the following relationship. Fig:3 Truss member in Tension where, = strain at a point ε u = axial displacement of any point along the length L By hook’s law, /ε =E σ Where, E = young’s modulus or modulus of elasticity. From the above relationship, and the relation, F = Aσ the deflection, can be found as δL, = FL/AE (1) δL Where, F = Applied load A = Cross-section area
The element may interconnect in a 2-D or 3-D configuration in space. The element is mechanically equivalent to a spring, since it has no stiffness against applied loads except those acting along the axis of the member. However, unlike a spring element, a element can be oriented in any direction in a plane, and the same element is capable of tension as well as compression. Fig: 2 A Truss Element 1.3 Stress – Strain relation: As stated earlier, all deflections in FEA are evaluated at the nodes. The stress and strain in an element is calculated by interpolation of deflection values shared by nodes of the element. Since the deflection equation of the element is clearly defined, calculation of stress and strain is rather simple matter. When a load F is applied on a truss member, the strain at a point is found by the following relationship. Fig:3 Truss member in Tension where, ε = strain at a point u = axial displacement of any point along the length L By hook’s law, σ /ε =E Where, E = young’s modulus or modulus of elasticity. From the above relationship, and the relation, F = Aσ the deflection, δL, can be found as δL = FL/AE (1) Where, F = Applied load A = Cross-section area
Introduction-to-Finite-element-method.docx