Surface loads: Define distributed loads on surface elements, calculate statically equivalent forces

The command allows do define constant or variably distributed loads on a plane or a cylindrical surface whereby the distributed load is immediately converted to statically equivalent forces on the corner nodes of the loaded elements.

The area and the direction of the distributed load are defined in a local coordinate system that is determined by 3 element nodes. The line from the first to the second node gives the local x-axis. The given 3 nodes also define the maximal expansion of the load area; it must completely be contained within the limits of the local coordinates given by the 3 points.

At first, all elements or surfaces of solid elements are determined, that lie on the plane and within the expansion of the local coordinate system, only the corner nodes of these elements respectively element surfaces are considered.

Four types of surface loads are distinguished:

Plane, p = constant

With this option, the loaded area may be a convex polygon of up to 8 points. Only constant load distribution is allowed (see following picture).

Plane, p = f (x, y)

With this option, the loaded area must be rectangular and parallel to the axis of the local coordinate system. All loaded elements must also be rectangular and parallel to the axis of the local coordinate system. The distributed load may be variable in both directions (see following picture).

Section of a circle

With this option, a rectangular section of a circle is loaded. Additional to the 3 reference nodes the ID of a defined cylindrical coordinate system must be given. All edges of loaded elements must be parallel to the axis of the given cylindrical system. The distributed load may be variable in both directions (see following picture).

Cylindrical surface

With this option, a rectangular section of a cylindrical surface is loaded. Additional to the 3 reference nodes the ID of a defined cylindrical coordinate system must be given. All edges of loaded elements must be parallel to the axis of the given cylindrical system. The distributed load may be variable in both directions (see following picture).

Each defined surface load is identified by 2 IDs, an index and a load set ID. The load set ID may be the same for different surface loads, but each surface load has a unique index. Pressing button “New index” gets the next unused index. Loads defined with command Element loads and Surface pressure are stored in the same data structure and use the same continuous range of indices. If the index of a stored surface load is given in the corresponding input field, with button “Show values” the stored values are displayed in the dialog box. These values may be plotted, deleted or modified. With button “Apply” the given values in the dialog are stored and the statically equivalent node forces are calculated and stored in the data structure. With button “Delete” stored values may be deleted.

Following dialog shows the available options:

Local coordinate system (3 nodes)

Plane (p = constant): A rectangular or polygonal bounded area with a constant load can be defined.

Plane (p = f (x, y)): A rectangular area with a variably distributed load can be defined. Edges of the load area and of the elements must be parallel to the axis of the local coordinate system.

Section of a circle: A rectangular area of a circle with a variably distributed load can be defined. Additionally to the 3 nodes, the ID of a defined cylindrical coordinate system must be given; the list box shows all defined coordinate systems. Edges of the loaded area and of the elements must be parallel to the axis of the cylindrical coordinate system.

Cylindrical surface: A rectangular area of a cylindrical surface with variably distributed loads can be defined. Additionally to the 3 nodes, the ID of a defined cylindrical coordinate system must be given; the list box shows all defined coordinate systems. Edges of the loaded area and of the elements must be parallel to the axis of the cylindrical coordinate system.

Nodes: The IDs of 3 nodes to define the local coordinate system must be given. After pressing button “Graphically” the 3 nodes can be selected graphically.

Limits of load area in the local coordinate system.

Relative (ul, ur, vl, vr): The left and right limits of the rectangular load area must be given relative to the length of the axis of the local coordinate system (0 £ u, v £ 1). The left and right limits may be the same to define a line or point load.

Absolute (xl, xr, yl, yr): The left and right limits of the rectangular load area must be given in coordinates of the local coordinate system.

Polygon: The (u, v) coordinates of up to 8 vertices of a polygon must be given relative to the length of the axis of the local coordinate system (0 £ u, v £ 1). The load area must be convex. This option is only available for a local coordinate system of type “Plane, p = constant”.

Graphically: After pressing this button, left and right limits of a rectangular area respectively of up to 8 vertices of a polygonal area can be selected graphically. The relative coordinates of the selected points are shown in the input field.

Plot: Pressing this button, the expansion of the loaded area is shown graphically.

Load distribution, load direction in the local coordinate system.

Constant: The value of a constant load distribution must be given.

Linearly: The load values at the 4 corners in the counter clockwise order must be given.

Quadratic: Additionally to the 4 values by linearly distribution 4 load values at the means of the 4 edges of the rectangular load area must be given.

Plot: Pressing this button, the load distribution is shown graphically.

Total load: If a value > 0 is given in the input field, the calculated forces are scaled so that the amount of the resultant is equal to this value.

Direction vector: The direction of the calculated force vectors must be given relative to the local coordinate system.

Index, Load set ID.

Index: The index of a new or already defined load group must be given. The list box shows all previously used indices for this kind of distributed loads. For the buttons “Plot” and “Delete” 2 indices of a range of indices may be given.

New index: Pressing this button the next unused index is shown in the input field for a new load group.

Show values: If the index of an already defined load group is given, the stored values of this group are displayed in the dialog after pressing this button.

Load set ID: A load set ID must be given for a new load group. The list box shows all previously used load set IDs.

Plot

Superimpose: If this option is marked, a new display list is used for plotting.

Plot load distribution: For the given index or range of indices the following is plotted: reference nodes and axis of a local coordinate system, load area and load distribution.

Plot forces: For the given index or range of indices the calculated statically equivalent forces are plotted.

Vlength: The plotted length of the largest vector respectively the maximal height for the load distribution must be given.

Color index: The color index for the plot must be given.

Annotate vectors: If this option is set, the vectors are labeled with the amount of the force vector.

Digits: If the vectors are to be labeled, the number of digits after the decimal point must be given.

Control

Pressing this button, the resultant of the force vectors is calculated. The components of the resultant and its position relative to the local coordinate system are displayed in the protocol window. The resultant is also graphically displayed.

Apply

The given values are stored in the internal data structure; the statically equivalent node forces are also calculated and stored. If there are already values stored under the given index, it is asked for overwriting.

Delete

All stored values for the given index or range of indices are deleted.