Question

Advanced structures questions:

Please provide short answers to the following questions:

1) Why do we use the PMPE (principle of minimum potential energy) versus the exact differential equation to derive the element stiffness equations?

2) What response modes are represented by a plate element? What are the response modes represented by a shell element?

3) What is the connectivity matrix? Why is it used in finite element software? Construct the connectivity matrix for a given structure.

3) What is the connectivity matrix? Why is it used in finite element software? Construct the connectivity matrix for a given structure.

Answer 1

1. Minimum Total Potential energy principle follows straightly from principle of virtual work (mainly for elastic materials). Total Potential energy is a function of displacement and it gets a staionary value ( i.e. minimum value) and solution foe displacvement can be obtained by finding the staionary value.For a conservative structural systems corresponding for an equilbrium state extremezs ( ie, minimum). For mimium point the sytem is stable condition.

Minimum Total Potential energy principle is used to find the solutions to problems which are imposible to solve exactly ( exact DE).This procedure is known as the Rayleigh Ritz method. In this method trial function can be assumed to be linear and can be solved easily

he accuracy of the solution 8.6.9 can be improved by using as the trial function a quadratic instead of a linear one.

2. Plane bending elements

It should be plane and the coordinates of the element nodes must be in one flat plane, the xy plane of the element.It should have thicness small than dimensions in plane and load should be perpendicular to the plane and moment should acts around the axis which is in the elemnt plane.

Direct stress component perpendicular to face is zero.(ie plane stress condition is satisfied)

Flat shell elements

It is the combination plane stress elemnt and bending elemnts

3. Connectivity Matrix(B)

It is a matrix help for asembling process in FEM.Row of the B will be the global nodes of elements.Column shows the local node number . Dimentions of this matrix B is N X (O +1)

N- Number of elemnts, O - Oder of elemnts