The Kreisselmaier-Steinhauser formulation is the more efficient of the two approaches and should be used whenever possible. The Kreisselmaier-Steinhauser formulation. Single eigenfrequencies from modal analysis and The Optimization Module supports two approaches for optimizing the eigenfrequencies: Perform a bandgap optimization that force modes away from a certain frequency. Maximize or minimize an eigenfrequency at a certain mode, and Typical uses of data from an eigenfrequency analysis during a topology optimization include the following:Ĭonstrain an eigenfrequency to be higher or lower than a given value, Modal eigenvalues are the simplest dynamic responses in structural analysis. As a result, the center of gravity calculated by the Optimization Module might not be the same as the center of gravity calculated by Abaqus/Standard or Abaqus/Explicit for example, if your model contains wire regions. The Optimization Module calculates the center of gravity using only the element types that are supported by topology optimization. When the Optimization Module calculates the center of gravity, it treats shell and membrane regions as three-dimensional regions by applying the thickness of the region. The Optimization Module applies the global coordinate system if you do not select a local coordinate system. If you select a local coordinate system, the Optimization Module uses both the direction of the axes and the position of the origin to recalculate the center of gravity. The design response can consider the center of gravity of the whole model or a region of the model.
When the Optimization Module calculates the center of gravity, the elements are scaled with the current relative density defined in your Abaqus model.įor example, you might want to constrain the center of gravity in the Y-direction so that it remains within a minimum and maximum range during the optimization. You cannot use strain energy as a constraint in your optimization. Topology optimization considers the total strain energy for all of the elements therefore, if you choose strain energy as an objective function, you must apply the objective to the entire model. In addition, you should always choose to maximize the strain energy if prescribed displacements are applied to your model. As a result, you should always choose to maximize the strain energy because attempting to minimize the strain energy can result in a stiff structure. However, if a load case is driven by a thermal field, strain energy decreases when the optimization modifies the structure to make it softer. If a load case is driven by forces or pressures, you should choose to minimize the strain energy to maximize the global stiffness. Compliance is the reciprocal of stiffness, and minimizing the compliance is equivalent to maximizing the global stiffness.
The compliance of a structure is a measure of its overall flexibility or stiffness and is defined as the sum of the strain energy of all the elements, for linear models, where is the displacement vector and is the global stiffness matrix.
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