Topology Optimization Utilities

TMR implements the class TopoProblem which is designed for topology optimization with ParOpt. This class can be set up to contain information about how to evaluate the objective function and constraints using a TACS.Assembler object. The adjoint derivative calculations for all members are implemented within the code.

  • class tmr.TMR.TopoProblem

    Creates and stores information for topology optimization problems

    addBucklingConstraint()

    Add buckling/natural frequency constraints

    addConstraints(self, case, funcs, offset, scale)

    Add a list of constraints for the specified load case. The constraints are specified as follows:

    scale[i]*(funcs[i] + offset[i]) >= 0

    Parameters

    • case (int) – Load case index to apply the constraints

    • funcs (list) – List of TACS.Function instances

    • offset (list) – List of floats specifying the constraint offset

    • scale (list) – List of scale value offsets

    addFrequencyConstraint()

    Add buckling/natural frequency constraints

    addLinearConstraints(self, vecs, offset)

    Add a set of load-case independent linear constraints represented by the provided vectors. The constraints are imposed as:

    dot(vecs[i], x) + offset[i] >= 0.0

    Parameters

    • vecs (list) – List of ParOpt.PVec instances

    • offset (list) – List of offsets for the constraints

    addStressConstraint(self, case, sc, offset=1.0, scale=1.0)

    Add a stress constraint formulated with stress reconstruction.

    scale*(sc + offset) >= 0

    Parameters

    • case (int) – Load case index

    • sc (StressConstraint) – Stress constraint instance

    • offset (float) – Constraint offset

    • scale (float) – Constraint scaling

    getAssembler(self)

    Get the Assembler object associated with the finest finite-element mesh

    Returns

    The finest Assembler ojbect

    Return type

    Assembler

    getFilter(self)

    Get the OctForest or QuadForest object associated with the finest topology opt discretization.

    Returns

    The forest associated with the finest mesh

    Return type

    OctForest or QuadForest

    getNumLoadCases(self)

    Get the number of load cases set in the optimization problem

    Returns

    The number of load cases

    Return type

    int

    initialize(self)

    Initialize the topology optimization instance. The optimization problem cannot be solved before this call. After this call, no more constraints can be added and the design problem is considered fixed.

    setF5EigenOutputFlags(self, freq, elem_type, flag)

    Set the output frequency and data for generating an .f5 file for eigenvector visualization. The elem_type and flag arguments dictate the type of data to be written to the .f5 file.

    Parameters

    • freq (int) – Optimization iteration frequency to write the file

    • elem_type (ElementType) – TACS element type

    • flag (int) – Flag indicating the type of element data to write

    setF5OutputFlags(self, freq, elem_type, flag)

    Set the output frequency and data for generating an .f5 file for solution visualization. The elem_type and flag arguments dictate the type of data to be written to the .f5 file.

    Parameters

    • freq (int) – Optimization iteration frequency to write the file

    • elem_type (ElementType) – TACS element type

    • flag (int) – Flag indicating the type of element data to write

    setInitDesignVars(self, pvec, lbvec, ubvec)

    Set the initial design variables and lower and upper bounds.

    Parameters

    • pvec (PVec) – ParOpt.PVec class storing the initial design vector

    • lbvec (PVec) – ParOpt.PVec class storing the lower bound vector

    • ubvec (PVec) – ParOpt.PVec class storing the upper bound vector

    setIterationCounter(self, count)

    Set an offset for the iteration counter. All iteration counts will start from the provided value.

    Parameters

    count (int) – Iteration counter offset >= 0

    setLoadCases(self, forces)

    Set the load cases to use within the optimization problem. The input list of forces is used as a vector of right-hand-sides within the TopoProblem solution method.

    Parameters

    forces (list) – A list of TACS.Vec vector instances

    setObjective(self, weights, funcs=None)

    Set the objective function for the design problem.

    If no list of functions is provided, the weighted compliance is assumed to be the objective. Otherwise a weighted sum of the functions evaluaed for each load case is used. Note that if a weight is set to zero, then the function and its gradient are not evaluated.

    Parameters

    • weights (list) – List of weights on the compliance or function

    • funcs (list) – Optional list of TACS.Function instances

    setPrefix(self, _prefix)

    Set the file prefix for output generated by TopoProblem.

    Parameters

    _prefix (str) – File name prefix

While you can create the TopoProblem from scratch, there are several utilities that can assist you with the creation of this object. createTopoProblem() generates a problem class with a specified hierarchy of octree or quadtree meshes. The construction of the finite-element discretization and the topology parametrization are problem-specific, so these are generated through a callback. Several additional helper functions are implemented to enable the creation of load vectors: computeVertexLoad() creates a load vector from forces at named vertices, computeTractionLoad() creates a load vector based on traction on named edges or faces. interpolateDesignVec() interpolates between design vectors after a refinement step.

  • tmr.TopOptUtils.createTopoProblem(forest, callback, filter_type, nlevels=2, repartition=True, design_vars_per_node=1, s=2.0, N=10, r0=0.05, lowest_order=2, ordering=5, scale_coordinate_factor=1.0)[source]

    Create a topology optimization problem instance and a hierarchy of meshes. This code takes in the OctForest or QuadForest on the finest mesh level and creates a series of coarser meshes for analysis and optimization. The discretization at each level is created via a callback function that generates the appropriate TACSCreator object and its associated filter (the QuadForest or OctForest on which the design parametrization is defined.) The code then creates a TMRTopoFilter class which stores information about the design parametrization and hierarchy. It creates a multigrid object and finally a TMRTopoProblem instance for optimization.

    The callback function takes in a forest object, corresponding to the finite- element discretization and returns a creator object and a filter object in the following form:

    creator, filter = callback(forest)

    Parameters

    • callback – A callback function that takes in the forest and returns the filter and the associated creator class

    • filter_type (str) – Type of filter to create

    • forest (TMROctForest or TMRQuadForest) – Forest type

    • repartition (bool) – Repartition the mesh

    • design_vars_per_node (int) – number of design variables for each node

    • s (float) – Matrix filter smoothing parameter

    • N (int) – Matrix filter approximation parameter

    • r0 (float) – Helmholtz filter radius

    • lowest_order (int) – Lowest order mesh to create

    • ordering – TACS Assembler ordering type

    • scale_coordinate_factor (float) – Scale all coordinates by this factor

    Returns

    The allocated topology optimization problem

    Return type

    problem (TopoProblem)

    tmr.TopOptUtils.computeVertexLoad(name, forest, assembler, point_force)[source]

    Add a load at vertices with the given name value. The assembler object must be created from the forest. The point_force must be equal to the number of variables per node in the assembler object.

    Parameters

    • name (str) – Name of the surface where the traction will be added

    • forest (QuadForest or OctForest) – Forest for the finite-element mesh

    • assembler (Assembler) – TACSAssembler object for the finite-element problem

    • point_force (list) – List of point forces to apply at the vertices

    Returns

    A force vector containing the point load

    Return type

    Vec

    tmr.TopOptUtils.computeTractionLoad(name, forest, assembler, trac)[source]

    Add a surface traction to all quadrants or octants that touch a face or edge with the given name. The assembler must be created from the provided forest. The list trac must have a traction for each face (6) for octants or each edge (4) for quadrants.

    Note: This code uses the fact that the getOctsWithName or getQuadsWithName returns the local face or edge index touching the surface or edge in the info member.

    Parameters

    • name (str) – Name of the surface where the traction will be added

    • forest (QuadForest or OctForest) – Forest for the finite-element mesh

    • assembler (Assembler) – TACSAssembler object for the finite-element problem

    • trac (list) – List of tractions, one for each possible face/edge orientation

    Returns

    A force vector containing the traction

    Return type

    Vec

    tmr.TopOptUtils.compute3DTractionLoad(name, forest, assembler, tr)[source]

    Add a constant surface traction to all octants that touch a face or edge with the given name.

    Parameters

    • forest (QuadForest or OctForest) – Forest for the finite-element mesh

    • name (str) – Name of the surface where the traction will be added

    • assembler (Assembler) – TACSAssembler object for the finite-element problem

    • tr (list) – The 3D components of the traction.

    Returns

    A force vector containing the traction

    Return type

    Vec

    tmr.TopOptUtils.interpolateDesignVec(orig_filter, orig_vec, new_filter, new_vec)[source]

    This function interpolates a design vector from the original design space defined on an OctForest or QuadForest and interpolates it to a new OctForest or QuadForest.

    This function is used after a mesh adaptation step to get the new design space.

    Parameters

    • orig_filter (OctForest or QuadForest) – Original filter Oct or QuadForest object

    • orig_vec (PVec) – Design variables on the original mesh in a ParOpt.PVec

    • new_filter (OctForest or QuadForest) – New filter Oct or QuadForest object

    • new_vec (PVec) – Design variables on the new mesh in a ParOpt.PVec (set on ouput)

    tmr.TopOptUtils.addNaturalFrequencyConstraint(problem, omega_min, **kwargs)[source]

    Add a natural frequency constraint to a TopoProblem optimization problem

    This function automatically sets good default arguments that can be overridden with keyword arguments passed in through kwargs.

    Parameters

    • problem (TopoProblem) – TopoProblem optimization problem

    • omega_min (float) – Minimum natural frequency, Hz

    • **kwargs – Frequency constraint parameters; check TMR documentation for more detail

    tmr.TopOptUtils.densityBasedRefine(forest, assembler, index=0, lower=0.05, upper=0.5, reverse=False, min_lev=0, max_lev=30)[source]

    Apply a density-based refinement criteria.

    This function takes in a Quad or OctForest that has been used for analysis and its corresponding Assembler object. It then uses the data set in the constitutive object to extract the density within each element. If the density falls below the the bound lower the element is coarsened, if the density exceeds upper the element is refined. If reverse is set, this scheme is reversed so low design values are refined. The refinement is applied directly to the forest.

    Parameters

    • forest (QuadForest or OctForest) – OctForest or QuadForest to refine

    • assembler (Assembler) – The TACS.Assembler object associated with forest

    • index (int) – The index used in the call to getDVOutputValue

    • lower (float) – the lower limit used for coarsening

    • upper (float) – the upper limit used for refinement

    • reverse (bool) – Reverse the refinement scheme

    • min_lev (int) – Minimum refinement level

    • max_lev (int) – Maximum refinement level

    class tmr.TopOptUtils.TopologyOptimizer(problem, options={})[source]

    Optimizer wrapper for topology optimization problems

    optimize()[source]

    Run the optimization problem using the settings. Runs either InteriorPoint or TrustRegion optimization problems

    Returns

    Optimized design point x

    Return type

    PVec

  • tmr.TMR.convertPVecToVec(pvec)

    Converts a ParOpt.PVec class to a TACS.Vec class.

    Parameters

    pvec (PVec) – A vector generated by TopoProblem

    Returns

    A TACS.Vec instance

    Return type

    Vec