用于任何形状 的复合 材料梁 的横截面分析的 Python 包_python_代码_下载

# Abdbeam : composites cross section analysis A Python package for the cross section analysis of composite material beams of any shape.  ## Main features These are a few things you can do with **Abdbeam**: * Use a fast thin-walled anisotropic composite beam theory including closed cells, open branches, shear connectors and booms (discrete stiffeners containing axial and torsional stiffnesses); * Recover replacement stiffnesses (EA, EIyy, EIzz, EIyz, GJ) and/or a full 4 x 4 stiffness matrix for beams with arbitrary layups and shapes; * Recover centroid and shear center locations; * Obtain internal load distributions (Nx, Nxy, Mx, My, Mxy for segments; Px and Tx for booms) for a large number of cross section load cases (defined by Px, My, Mz, Tz, Vy and Vz section loads); * Plot cross sections, their properties and internal loads. ## Installing Install using PyPI ([Python package index](https://pypi.org/project/abdbeam)) : ```sh pip install abdbeam ``` ## Source and Documentation The source code is hosted on GitHub at https://github.com/victorazzo/abdbeam and the documentation can be found at https://docs.abdbeam.org. ## Dependencies - [NumPy](https://www.numpy.org) - [Pandas](https://pandas.pydata.org) - [Matplotlib](https://matplotlib.org) ## Example Let's use **Abdbeam** to analyze the cross section with two closed cells below: <img src="https://user-images.githubusercontent.com/24232637/50049830-266c6380-00bc-11e9-808d-97896d3f3e16.png" width="400"> Start creating the section materials, its points and segments (we'll also calculate the section properties and request a summary at the end): ```python import abdbeam as ab sc = ab.Section() # Create a materials dictionary: mts = dict() mts[1] = ab.Laminate() ply_mat = ab.PlyMaterial(0.166666, 148000, 9650, 4550, 0.3) mts[1].ply_materials[1] = ply_mat mts[1].plies = [[0,1]]*6 + [[45,1]]*6 # Create a points dictionary based on Y and Z point coordinates: pts = dict() pts[1] = ab.Point(0, -35) pts[2] = ab.Point(-50, -35) pts[3] = ab.Point(-50, 35) pts[4] = ab.Point(0, 35) pts[5] = ab.Point(50, 35) pts[6] = ab.Point(50, -35) # Create a segments dictionary referencing point and material ids: sgs = dict() sgs[1] = ab.Segment(1,2,1) sgs[2] = ab.Segment(2,3,1) sgs[3] = ab.Segment(3,4,1) sgs[4] = ab.Segment(4,1,1) sgs[5] = ab.Segment(4,5,1) sgs[6] = ab.Segment(5,6,1) sgs[7] = ab.Segment(6,1,1) # Point the dictionaries to the section sc.materials = mts sc.points = pts sc.segments = sgs # Calculate and output section properties sc.calculate_properties() sc.summary() ``` Which prints: ```sh Section Summary =============== Number of points: 6 Number of segments: 7 Number of cells: 2 Centroid -------- yc = -2.67780636e-01 zc = 0.00000000e+00 Shear Center ------------ ys = 2.35301214e-03 zs = -1.45758049e-03 Replacement Stiffnesses ----------------------- EA = 6.80329523e+07 EIyy = 5.24834340e+10 EIzz = 8.36408748e+10 EIyz = 0.00000000e+00 GJ = 1.23762317e+10 EImax = 8.36408748e+10 EImin = 5.24834340e+10 Angle = 0.00000000e+00 [P_c] - Beam Stiffness Matrix at the Centroid --------------------------------------------- [[ 6.80329523e+07 0.00000000e+00 2.46320132e+05 -1.43701515e+08] [ 0.00000000e+00 5.24834340e+10 0.00000000e+00 0.00000000e+00] [ 2.46320132e+05 0.00000000e+00 8.36408748e+10 -2.12142163e+07] [-1.43701515e+08 0.00000000e+00 -2.12142163e+07 1.23762317e+10]] [W_c] - Beam Compliance Matrix at the Centroid ---------------------------------------------- [[1.50683149e-08 0.00000000e+00 1.66286490e-28 1.74959530e-10] [0.00000000e+00 1.90536313e-11 0.00000000e+00 0.00000000e+00] [1.57282135e-25 0.00000000e+00 1.19558821e-11 2.04936911e-14] [1.74959530e-10 0.00000000e+00 2.04936911e-14 8.28315446e-11]] [P] - Beam Stiffness Matrix at the Origin ----------------------------------------- [[ 6.80329523e+07 0.00000000e+00 -1.79715871e+07 -1.43701515e+08] [ 0.00000000e+00 5.24834340e+10 0.00000000e+00 0.00000000e+00] [-1.79715871e+07 0.00000000e+00 8.36456213e+10 1.72662667e+07] [-1.43701515e+08 0.00000000e+00 1.72662667e+07 1.23762317e+10]] [W] - Beam Compliance Matrix at the Origin ------------------------------------------ [[1.50691722e-08 0.00000000e+00 3.20155371e-12 1.74965018e-10] [0.00000000e+00 1.90536313e-11 0.00000000e+00 0.00000000e+00] [3.20155371e-12 0.00000000e+00 1.19558821e-11 2.04936911e-14] [1.74965018e-10 0.00000000e+00 2.04936911e-14 8.28315446e-11]] ``` Now let's create two load cases (101 and 102) and calculate their internal loads: ```python sc.loads = dict() sc.loads[101] = ab.Load(My=5e6) sc.loads[102] = ab.Load(Tx=250000, Vz=5000.0) sc.calculate_internal_loads() ``` Next print all internal loads (which outputs a lot of data we'll not show here): ```python sc.print_internal_loads() ``` Or access the Pandas dataframe containing these internal loads directly: ```python df = sc.sgs_int_lds_df ``` Next plot the cross section and its properties (we'll show the segment orientations, hide legends, change the centroid , shear center and principal axis colors and use a custom figure size): ```python ab.plot_section(sc, segment_coord=True, title='Abdbeam - Example', legend=False, prop_color='#471365', figsize=(5.12, 3.84)) ```  Finally, plot Nx and Nxy for load case 101 (we'll change the matplotlib contour palette, reduce the internal load diagram scale, and use a custom figure size): ```python ab.plot_section_loads(sc, 101, contour_color='viridis', diagram_scale=0.7, int_load_list=['Nx', 'Nxy'], figsize=(5.12, 3.84)) ```  ## License BSD-3 ## Contribute **Abdbeam** is at its early development stages and we encourage you to pitch in and [contribute on GitHub](https://github.com/victorazzo/abdbeam). Guidelines for contributors are in the works, so stay tuned. ## Theory For the theory behind Abdbeam, the most complete reference is: [Victorazzo DS, De Jesus A. A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections. Journal of Reinforced Plastics and Composites. 2016 Dec;35(23):1696-711.](https://journals.sagepub.com/doi/abs/10.1177/0731684416665493) These are also great references on its originating theory: * [Kollár LP, Springer GS. Mechanics of composite structures. Cambridge university press; 2003 Feb 17.](https://www.amazon.com/Mechanics-Composite-Structures-L%C3%A1szl%C3%B3-Koll%C3%A1r/dp/0521126908/ref=sr_1_1?ie=UTF8&qid=1544936929&sr=8-1&keywords=Mechanics+of+composite+structures) * [Kollár LP and Pluzsik A. Analysis of thin-walled composite beams with arbitrary layup. J Reinf Plast Compos 2002; 21: 1423–1465.](https://journals.sagepub.com/doi/abs/10.1177/0731684402021016928) Note: the effects of shear deformation and restrained warping are assumed negligible in **Abdbeam**. Check the references above for more details.