MaFoDeM

MaFoDeM = Matrix Form of Displacement Method

MaFoDeM user guide

Introduction

Application MaFoDeM serves for linear static analysis of the displacement and stress of plane bar structures. Calculation procedure is based on Direct Stiffness Method (also known as Displacement Method or Matrix Stiffness Method). In this implementation both strains of the beam are included (normal strain and shear strain).

A structure model and loads is possible to specify in the application according to procedure of direct stiffness method. Calculation will be done automatically after set up of model and load or after any change. This is unique property and it provides possibility to easy show the influence of any change. Another advantage is capability to show all vectors and matrices used for solution.

Application launching

Application can be launched by click on file mafodem.jar. If application is launched successfully, working plane XZ will be shown, see fig. 1.

Fig. 1 Working plane

Used coordinate system including positive direction is shown in the working plane. The convention of positive forces and displacements is linked with this coordinate system. The mouse cursor coordinates and another informations (explained below) are shown in the bottom panel.

Problem

We have plane frame with geometry, physical properties and loads given by scheme on fig. 2.

Fig. 2 Given plane frame

Solution of this frame in application MaFoDeM includes following parts:

• creation of nodes, e.g. points, where are the bars connected and where are edges of the bars (free ends);
• setting up of bars, which means specification of nodes, physical parameters and type of node connections;
• adding loads;
• observing results;

Creation of nodes

Before nodes creation its positions have to be found according to direct stiffness method. If it is known, nodes must be specified by coordinates in working plane. Also restraints are necessary to enter. According to given frame, see fig. 2, we can write following table of nodes:

Node will be created using dialog from application menu Node -- New. It shows dialog New Node, see fig. 3.

Fig. 3 Dialog New Node

Dialog provides specification of node position in two ways: by click on a point in working plane after using button Pick or by entering of coordinates in text fields confirmed by button Apply. Restraint can be specified independently.

We will create the first node by following way: in to the coordinate text fields X and Z we will write 0. Then we check restraint X translation and Z translation. Third checkbox rotation retain unchecked. Finnaly we click on button Apply. We will obtain confirm message Node created in field status after successfull creation. Next nodes we will create in the similar way.

Notes:
Coordinates can be entered in the format with dot. Scientific format of a number is possible too, for example 1.25E-3.
In the case of wrong specification of the resraints, use the dialog from menu Node -- Change Attributes.
Node can be removed after its selection by mouse with calling menu Node -- Delete. Connected nodes cannot be removed.

Change of view

After creation of nodes the view of working plane can be conformed to your own requirements with help of dialog View -- View Panel. Dialog View Panel will be shown, see fig. 4.

Fig. 4 Dialog View Panel

This dialog allows to change settings of the working plane. For example the button All in the upper part zoom will make all nodes visible. Next you can use buttons for zooming and shifting (part pan). In the bottom part of the panel the buttons for viewing of internal forces functions and displacements are placed.

After nodes creation and after the change of view the working plane can looks like on fig. 5

Fig. 5 Working plane after nodes creation

All created nodes including their restraints are shown in the figure. In the bottom panel in the text field Nodes number 5 with zero in the brackets is shown. Number five means a number of created nodes and zero a number of selected nodes. Node can be selected by click on its square. More than one node can be selected with help of the key Ctrl.

Creation of bars

A bar can be created by specification of two nodes, physical properties and type of a node connection. There are two types of node connection: rigid and with hinge. Specification can be done by dialog Bar -- New. Dialog New Bar will be shown, see fig. 6

Fig. 6 Dialog New Bar

Initially specify physical properties according to given frame (fig. 2). First bar, which connects node 0 with node 1, has following parametrers:

Notes:
Parameters h and c_T are irelevant according to given frame (there are no thermal load). However any number have to be specified (for example 1).
If you want to suppress an influence of shear strain enter in A_kappa value 1E99.

Next step is specification of connection type. There are two possibilities for first bar, see fig. 2. Left node is hinged, therefore bar can be connected by rigid connection and also by hinge. Choose hinge by checking hinge at node[a]. Right node must be rigid connected. Then the resulting dialog before first bar creation looks like fig. 7.

Fig. 7 Dialog New Bar after specification of the first bar

Finally two nodes have to be specified after using the button Pick. First application will make check up of entered values. In the case of specification without mistakes the dialog will report Pick first node, see fig. 8

Fig. 8 Dialog New Bar (Nový Prut) after using the button Pick

The picking of nodes will be done by click on their squares in working plane. Right pick is confirmed by report Pick second node. After successful picking the report Bar created will be shown.

Second bar has the same parameters but different type of node connection. Hinge is neccessary to put on the right end of the bar and left have to be rigid. After this change nodes can be picked.

Third bar (horizontal cantilever) has the same parameters too. Use rigid connection at both ends.

The last bar (column) has different parameters than previous. Therefore we have to change specified values. Opening of input fields will be done by using button Edit. After entering new parameters use button Pick again. Pick nodes with rigid connections. Resulting state is shown in fig. 9

Fig. 9 Working plane after bars creation

The figure shows all created bars. Every bar has a bill which indicates the bar orientation. The orientation is significant for local coordination system of a bar and for its internal forces. In the bottom panel Bars the count of created bars is written. Additionally there is a text field DOFs, which shows number of degrees of freedom of the model.

Notes:
In the case of wrong specification of a bar use dialog Bar -- Change Attributes.
After its picking a bar can be deleted by Bar -- Delete.

Continuous load

Not yet written.