Posted On :

1 Potential energy in elastic bodies 2 Principle of Minimum Potential Energy

**PRINCIPLE OF STATIONERY TOTAL POTENTIAL (PSTP)**

**1 Potential energy in elastic bodies**

Potential energy is the capacity to do the work by the force acting on deformable bodies; the forces acting on a body may be classified as external forces and internal forces. External forces are the applied loads while internal force is the stresses developed in the body. Hence the total potential energy is the sum of internal and external potential energy.

Consider a spring mass system let its stiffness be k and length L, due to a force P let it extend

by u

The load P moves down by distance u. hence it loses its capacity to do work by P u. the external potential energy in this case is given by.

H = -P u

Average force = Ku/2

The energy stored in the spring due to strain = Average force x Deflection

= Ku/2 x u

Total potential energy in the spring = K u2- P u

**2 Principle of Minimum Potential Energy**

From the expression for total potential energy

Hence we can conclude that a deformable body is in equilibrium when the potential energy is having stationary value.

Hence the principle of minimum potential energy states among all the displacement equations that internal compatibility and the boundary condition those that also satisfy the equation of equilibrium make the potential energy a minimum is a stable system

**Problem 7**

Given: For the spring system shown above,

k1 100 N / mm,

k2 200 N / mm,

k3 100 N / mm

P 500 N,

u1 0

u4 0

Find: (a) The global stiffness matrix

(b) Displacements of nodes 2 and 3

(c) The reaction forces at nodes 1 and 4

(d) the force in the spring 2

Solution:

(a) The element stiffness matrices are

**Problem 8**

For the spring system with arbitrarily numbered nodes and elements, as shown above, find the global stiffness matrix.

** Solution**:

First we construct the following

**Element Connectivity Table**

**Element : Node i (1) : Node j (2)**

1 4 2

2 2 3

3 3 5

4 2 1

Which specifies the global node numbers corresponding to the local node numbers for each element? Then we can write the element stiffness matrices as follows

Finally, applying the superposition method, we obtain the global stiffness matrix as follows

We may note that N1 and N2 obey the definition of shape function that is the shape function will have a value equal to unity at the node to which it belong and zero value at other nodes.

Tags : Mechanical - Finite Element Analysis - Finite Element Formulation of Boundary Value Problems

Last 30 days 65 views
Related words : ### What is Principle Of Stationery Total Potential (PSTP) Define Principle Of Stationery Total Potential (PSTP) Definition of Principle Of Stationery Total Potential (PSTP) where how
meaning of Principle Of Stationery Total Potential (PSTP)
lecturing notes for Principle Of Stationery Total Potential (PSTP) lecture notes question and answer for Principle Of Stationery Total Potential (PSTP) answer
Principle Of Stationery Total Potential (PSTP) study material Principle Of Stationery Total Potential (PSTP) assignment Principle Of Stationery Total Potential (PSTP) reference description of Principle Of Stationery Total Potential (PSTP)
explanation of Principle Of Stationery Total Potential (PSTP) brief detail of Principle Of Stationery Total Potential (PSTP) easy explanation solution Principle Of Stationery Total Potential (PSTP) wiki
Principle Of Stationery Total Potential (PSTP) wikipedia how why is who were when is when did where did Principle Of Stationery Total Potential (PSTP) list of Principle Of Stationery Total Potential (PSTP) school assignment college assignment
Principle Of Stationery Total Potential (PSTP) college notes school notes kids with diagram or figure or image difference between Principle Of Stationery Total Potential (PSTP) www.readorrefer.in - Read Or Refer

Recent New Topics :