veiguf / easybeam Goto Github PK

• Define boundary conditions and loads via node number and global degree of freedom, i.e. x, y, rot
• Fix code so warnings no longer received or suppress these
• Mass matrix, consistant and lumped?
• Add eigenfrequency solver
• The scale value should not be used in calculateStress() and should be only a property of plotting
• Remove nEl from plots so that mesh plots can be done before initialize()
• rename nSteps, e.g. nColorDivisions, nColorDiv, nColorSegments, nColorSeg
• Separate solve() into subfunctions, e.g. assemble(), elemstiff(), elemmass(), etc
• Consistent name for component to plot? Currently "component" and "stress"
• Plot with boundary condition and loads
• Plot boundary condition and loads with symbols instead of description
• Plot with dof?
• Documentation with roadmap
• Calculate area moment of inertia via geometrical shape
• Ability to have different cross-sectional geometries and materials via element groups.
• Remove initialize()
• Revamp logo, i.e. B
• Sparse solving
• Plotting of matrix structure, see matplotlib.pyplot.imshow
• Plot shape functions
• Plot internal shear force and bending moment
• Calculate load from selfweight
• Calculate shear area for Timoshenko matrices (or enter by hand)
• Eigensolver for unconstrainted structures and Timoshenko beams, i.e. eig solve, sort, etc.
• Validation of results with e.g. Kratos Multiphysics, NASTRAN, or ANSYS
• Added mass points, i.e. give node to which mass will be added. (also mass moment of inertia?)
• Add legend to show geometric scale? I.e. |----| 1 mm for geometry and |----| 1 m for displacement
• Design sensitivities
• Generalize sensitivity computations
• Sensitivity plots
• Anisotropic beam

Further ideas - Long term

• Timoshenko element descriptions
• Material library
• Element library?
• VTK plots
• 3D
• ground structure optimization

Currently nEl strain--displacement matrices are constructed in the initialization of the model. For large models, this requires relatively large amounts of computational effort.

This could be moved to a postprocessing step and loaded into the memory only at the time of the strain calculation (or directly to stress calculation). This would have the added benefit of not being used at all in modal analysis where it is not used.

Analogously, one could consider similar speed up measures for TransMat and ShapeMat

Overwriting of self.El causing issues for the implementation of SA sensitivity analysis. This is kind of dirty. Can this be avoided?

    def Initialize(self):
        self.N = np.array(self.N, dtype=float)
        El = np.array(self.El)
        self.PropID = El[:, 2]
        self.El = np.array(El[:, 0:2], dtype=int)

In the current code, the largest time expenditure is the assembling of the system matrices: BeamAnalysis.py 180-184.

    def Assemble(self, MatElem):
        Matrix = np.zeros([self.nNDoF*self.nN, self.nNDoF*self.nN])
        for i in range(self.nEl):
            Matrix += self.L[i][email protected][i].T@MatElem(i)@self.T[i]@self.L[i]
        return Matrix

The global matrix is assemble by the rotating and extending the element matrix to the global coordinate system.

It will be faster to rotate but not expand the element matrices and assigning it via an index, i.e.

Matrix[dof[i], dof[i]] += self.T[i].T@MatElem(i)@self.T[i]

where dof[i] is a vector of global dofs for the ith element.

This avoids two multiplication operations and the memory needed for the larger elements.

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See here.

Just found that the difference, especially in the mode shape, between Euler-Bernoulli and Timoshenko is very large.

There are also differences in

• numpy.linalg.eig
• scipy.linalg.eig
• numpy.linalg.eigh
• scipy.linalg.eigh

We should look into this and then validate a couple examples analytically or with FEA.