Systems and methods for topology and shape optimization for modeling of a physical object

A computer-implemented simulation method executable on one or more processors configured to generate a model of a physical system, the simulation method optimizing a shape of a geometrical representation of a physical object being modeled, the simulation method comprising the acts of:

• receiving initial geometry data representing an initial geometry of the physical object being modeled;
• defining equation data representing physical properties for one or more portions of the initial geometry;
• receiving, via one or more graphical user interfaces configured for display on one or more display devices, user inputs representing one or more shape optimization settings including control variable settings defining a maximum displacement and polynomial order and user selections of one or more portions of the initial geometry being shape optimized;
• generating, via the one or more processors, discretized model data representing a discretized model of the physical object being modeled based on the initial geometry, the discretized model including a mesh based on (i) the initial geometry and mesh element node coordinates for portions of the initial geometry to be shape optimized based on control variables, and (ii) a shape optimization objective expression;
• defining shape optimization solver settings and a shape optimization objective expression for a shape optimization solver, the shape optimization objective expression being at least partially determined by one or more control variables;
• generating, via the one or more processors, updated control variable values based on the defined shape optimization solver settings;
• performing, via the one or more processors, an iterative operation including solving the shape optimization objective expression based at least partially on the updated control variable values, the iterative operation continuing until a defined maximum number of iterations have been performed or until at least one shape optimization solver determines that an optimized shape solution has been achieved;
• and
• storing optimized shape solution data representing the optimized shape solution on a computer memory device, the optimized shape solution including a shape optimized mesh corresponding to the optimized shape solution or a shape solution based on more than one iteration of solving the shape optimization objective expression,
• wherein the control variables are Bernstein polynomial coefficients generated by the one or more processors in response to receiving the user selections of the one or more portions of the initial geometry being shape optimized and in response to receiving the user inputs representing the control variable settings.

A computer-implemented simulation post-processing method applied to a mesh dataset from a topology optimization including material volume factor value data and mesh data, the method generating a filtered mesh dataset based on the values of the material volume factors such that only mesh elements meeting one or more criteria with respect to material volume factor values are retained in a filtered mesh dataset, the method comprising the acts of:

• selecting an initial mesh dataset;
• defining a material volume factor expression;
• defining one or more criteria including one or more bounds for mesh elements or mesh nodes to be included in the filtered mesh, the one or more bounds based on material volume factor values associated with the mesh elements or mesh nodes that are applied in the defined material volume factor expression;
• generating, via one or more processors, the filtered mesh dataset including the mesh elements or mesh nodes meeting the defined one or more criteria for the values associated with the mesh elements or mesh nodes that are applied in the defined material volume factor expression;
• and
• generating, via one or more processors, a graphical representation of the filtered mesh dataset for display in a graphical user interface associated with one or more display devices,
• wherein the mesh dataset includes named selections and the association of named selections with mesh elements is maintained in a modified filtered mesh dataset, and wherein the named selections are optionally presented in the graphical representation.

A computer-implemented simulation method executable on one or more processors configured to generate a model of a physical system, the simulation method optimizing a shape of a geometrical representation of a physical object being modeled, the simulation method comprising the acts of:

• receiving initial geometry data representing an initial geometry of the physical object being modeled;
• defining equation data representing physical properties for one or more portions of the initial geometry;
• receiving, via one or more graphical user interfaces configured for display on one or more display devices, first user inputs representing one or more shape optimization settings including control variable settings and user selections of one or more portions of the initial geometry being shape optimized;
• receiving, via one or more graphical user interfaces configured for display on one or more display devices, second user inputs representing boundary settings for designating non-optimized boundaries allowing mesh nodes of a non-optimized boundary to move tangentially on the non-optimized boundary such that displacement of a shape optimized boundary connected to the non-optimized boundary is tangential to the non-optimized boundary;
• generating, via the one or more processors, discretized model data representing a discretized model of the physical object being modeled based on the initial geometry, the discretized model including a mesh based on (i) the initial geometry and mesh element node coordinates for portions of the initial geometry to be shape optimized based on control variables, and (ii) a shape optimization objective expression;
• defining shape optimization solver settings and a shape optimization objective expression for a shape optimization solver, the shape optimization objective expression being at least partially determined by one or more control variables;
• generating, via the one or more processors, updated control variable values based on the defined shape optimization solver settings;
• performing, via the one or more processors, an iterative operation including solving the shape optimization objective expression based at least partially on the updated control variable values, the iterative operation continuing until a defined maximum number of iterations have been performed or until at least one shape optimization solver determines that an optimized shape solution has been achieved;
• and
• storing optimized shape solution data representing the optimized shape solution on a computer memory device, the optimized shape solution including a shape optimized mesh corresponding to the optimized shape solution or a shape solution based on more than one iteration of solving the shape optimization objective expression.