Deformation module
The deformation module is used to calculate the deformations and the resulting stresses of flat panels due to loading perpendicular to the panel plane ([1], [2], [3]). As with the modulus of stability, the calculations only provide correct results for symmetrical laminates due to the approaches used. The mechanical behavior of the panel is illustrated using the same approach functions as in the consideration of the stability behavior. It is possible to add stiffening elements to the panel. In the current version, a constant surface load can be applied to the entire area of the panel or point loads can be applied to the panel. These loads can also be combined.
Due to the assumed symmetry of the laminate, the calculations in the deformation modulus of eLamX² are based exclusively on the bending stiffness matrix
The model sizes are entered separately for the panel made of the defined laminate and the additionally applied stiffening elements.
First, a flat rectangular panel is modeled from the specified laminate by specifying the length and width. The desired boundary conditions must then be specified. The default setting is for the panel to be hinged on all sides. In addition, further boundary conditions can be selected by clicking on the drop-down menu, which are indicated by corresponding symbols. The normal loads acting on the plate must be specified below. A combination of loads is possible, which can be defined in the load dialog.
In the current version of eLamX², point loads and constant surface loads can be defined as loads on the plate.
The load is applied exclusively to the plate. Any stiffening elements applied have no influence on the load definition. The effective direction of the load corresponds to the orientation of the z-axis. A positive load acts in the positive z-direction, a negative load in the negative z-direction. It should be noted at this point that the underlying calculation approach is based on the assumptions of Kirchhoff's plate theory. Small deflections and corresponding loads are therefore assumed. A load position corresponding to the plate coordinate system must be specified for the point load.
The position specification is absolute with its origin (
The surface load acts constantly on the entire panel area. The force to be specified corresponds to the force per unit area. As in the stability module, the scoring method is used to calculate the deformation of the plate by using global approach functions. Increasing the number of terms to be specified for the approach functions increases the accuracy, but also the calculation time. To ensure sufficient calculation accuracy, the number of terms should not be set too low. The number of terms used should be selected so that it is greater than the larger value of the aspect ratio length/width or width/length.
The calculations are performed with consideration of the bending-drilling coupling within the laminate.
The loads can be edited, copied or deleted by right-clicking on the corresponding load.
Analoguous to the stability module, the dropbox D matrix options allows to set various options regarding the bending stiffness matrix
With the option Original, the original bending stiffness matrix
To ensure closed-form analytical solutions, orthotropic or quasiorthotropic material behavior is assumed in many calculation methods and literature. In these methods, the influence of the bending-drilling coupling through the terms
With this option, the bending stiffness matrix
This option allows to treat asymmetrical laminates with an approximate solution. For symmetric laminates, the option has no effect compared to the Original option, as
Pressing the Calculate button starts the calculation within the deformation module. Before the calculation, the ABD matrix of the defined laminate is automatically calculated and checked to see whether the laminate is symmetrical with respect to the center plane. In the case of an asymmetrical laminate structure, the following warning message is displayed, unless the option for using the
Despite the warning message, the deformation module of eLamX² can also be called up for asymmetrical laminates. In this case, the user is responsible for checking the meaningfulness of the results.
The minimum and maximum deflection of the plate are given as standard as the result of the calculations with the eLamX² deformation module. Using the selection list shown further results will be made available for display in future versions of eLamX².
It is also possible to specify a scaling factor for the deflection in the graphical output. By default, this value is one. This corresponds to the normalization to the maximum value occurring in the plate.
In addition to the numerical output, the selected result is displayed graphically. The display is three-dimensional according to the Cartesian coordinate system shown. Here x and y denote the axes of the plate plane. The z-axis points in the thickness direction of the laminate. The stiffening elements are shown in gray. In the graphical output, the stiffeners are positioned as shown in the model. Their center of gravity is in the middle plane of the panel. The deflection is displayed in colors ranging from red to blue. The color red indicates the largest deflection in the positive z-direction and blue the largest deflection in the negative z-direction. This results in different color distributions depending on the direction of the applied load.
The model can be moved, rotated and zoomed to any position by holding down the mouse buttons.
- Turning
- Zoom
- Move
These buttons can be used to edit the result view of the rectangular plate. The top three buttons can be used to display the three planes of the three-dimensional Cartesian coordinate system. In addition, an isometric display and an adjustment of the display to the existing window size are possible.
- View of the x-y plane
- View of the x-z plane
- View of the y-z plane
- Isometric representation
- Adaptation to window size
- Display of the acting forces
- Show the legend or information box
The stiffening wizard is used to define stiffening elements. You must first select the cross-section of the stiffener. The following cross-sections are available for this:
- Free stiffener cross-section by defining the elastic modulus E, the second-order moment of inertia I, shear modulus G and torsional area moment J
- I-cross-section defined by height, width, elastic modulus E and shear modulus G
- T-cross-section defined by flange height, flange width, web height, web width, elastic modulus E and shear modulus G
The further modeling of the stiffening elements depends on the respective type.
In general, the direction of the reinforcement must be specified. The orientation indicates the axis of the plate to which the stiffening element should run parallel. In addition to the mechanical and geometric characteristics of the stiffening elements, their position must also be specified. This value is absolute and therefore not linked to the size of the plate. They refer to the coordinate system shown in the 3D view. If the dimensions of the plate are changed, the position of the stiffening elements remains constant. Only arrangements of stiffening elements within the plate geometry make sense. If stringers are nevertheless defined outside the plate boundaries, these are initially displayed in the table of stiffening elements and in the 3D view, but are not taken into account during the calculation.
It is possible to subsequently change the position, direction or the entered data within the table display or the properties window in the main window. Right-click on the stiffener to edit, copy or delete it.
If a stiffener without torsional stiffness is to be modeled, this is done by setting G, J or both to zero. Each stiffening element can have different material and geometry parameters.
[1] J.N. Reddy. Mechanics of Laminated Composite Plates and Shells- Theory and Analysis. CRC Press, Boca Raton, 2. auflage edition, 2003.
[2] O. Hennig. Umsetzung eines Moduls zur Beschreibung des mechanischen Verhaltens von Compositeplatten für das Programm eLamX. ILR –LFT G 08-07, Technische Universität Dresden, Mai 2009.
[3] A. Hauffe. Neue Methode zur schnellen Beulberechnung von geschichteten Platten. ILR-LFT 09-13IR, Technische Universität Dresden, July 2009.