Hi, I’m following the book “Practical Finite Element Analysis for mechanical engineers”, and in section 14.7.2 I find an example where the base of a fitting is in contact with a plate and this contact is modeled as a point-to-point linear contact:
All the nodes of the fitting’s base have their own MPCs. The plate is not represented in the model, the MPC linear contacts are grounded.
I’m using PreProMax for the FEM except for the MPCs. The CalculiX manual mentions in point 6.7.2 that MPCs are done with *EQUATION and SPCs, so I’m crafting with a Python script the additional code needed for the .inp file.
I’m creating two groups of new nodes corresponding to the ones in the base of the fitting. A first group is created (and placed in the exact same place as the original ones of the base of the fitting) and I add some SPCs to constrain their x,y,z degrees of freedom with *BOUNDARY. The second group of nodes are as well created in the original position of the ones of the base and their x and y DOF restricted with *BOUNDARY.
Finally, I use *EQUATION for each node of the base to say something like:
-w_555 + w_1555 + w_2555 = 0
Where:
- w_555 would be the z component of the node 555 (one of the nodes of the base)
- w_1555 is the z component of the fully constrained new node 1555
- w_2555 is is the z component of the new node 2555 whose z is unconstrained.
So I expect that w_555 = w_1555 + w_2555, and since w_1555 is fully constrained, only w_2555 move. The problem is that it’s moving up and down, I would expect it to move only upwards and not be able to go below w_1555. How do I do that?
I have uploaded all my files here for easier inspection:
The code is the following:
from collections import namedtuple
Point = namedtuple('Point', ['x', 'y', 'z'])
def MPC(nodes, base_nodes, movable_nodes):
"""
These must be defined before the first *STEP in the Calculix .inp file
*EQUATION
- Number of terms in the equation
- Node number of the first variable.
- Degree of freedom at above node for the first variable.
- Value of the coefficient of the first variable.
"""
equations = []
for node_id, base_node_id, mv_node_id in zip(nodes, base_nodes, movable_nodes):
eq = (
f"** MY EQUATIONS\n*EQUATION\n"
f"3\n"
f"{node_id}, {3}, -1, {base_node_id}, {3}, 1, {mv_node_id}, {3}, 1\n")
equations.append(eq)
return "".join(equations)
def get_nodes_map(calculix_filename):
"""
Load CalculiX .inp file to parse its nodes and return
something like: {'5462': Point(), ...}
"""
nodes_map = {}
found = False
with open(calculix_filename, "r") as f:
for line in f.readlines():
line = line.strip()
if found:
if "**" in line:
break
else:
node_id, x, y, z = line.split(', ')
nodes_map[node_id] = Point(x=float(x), y=float(y), z=float(z))
else:
if "*Node" in line:
found = True
print("Found where the nodes are")
else:
continue
return nodes_map
def gen_nodes(first_node_id, query_nodes, calculix_filename="Fitting_fea.inp"):
"""
Create new nodes (with id starting at `first_node_id`) positioned in
the same place of the query nodes.
"""
nodes_map = get_nodes_map(calculix_filename)
s = "** MY NODES\n*Node\n"
dummy_nodes = []
for i,node_id in enumerate(query_nodes):
x,y,z = nodes_map[str(node_id)]
dummy_nodes.append(first_node_id+i)
s += f"{first_node_id+i}, {x}, {y}, {z}\n"
return s, dummy_nodes
def constrain_dofs(nodes):
"""
These must be defined inside a *STEP
"""
s = "** MY BOUNDARIES\n*BOUNDARY\n"
for node_id in nodes:
s += f"{node_id}, 1, 2\n"
return s
def fix_base(nodes):
s = "** Name: MY BOUNDARIES\n*BOUNDARY\n"
for node_id in nodes:
s += f"{node_id}, 1, 3, 0\n" # constrain x, y, z
return s
# The follwing list of nodes was extracted from an exported CalculiX file based on a Node Set
nodes = [
70, 71, 74, 75, 80, 81, 84, 85, 448, 452, 453, 454, 455, 456, 457, 458,
459, 460, 461, 474, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 615, 616,
617, 618, 619, 620, 621, 622, 623, 624, 637, 638, 639, 640, 641, 642, 643, 644,
645, 646, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661,
662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 2586, 2587, 2588, 2589,
2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 2600, 2601, 2602, 2603, 2604, 2605,
2606, 2607, 2608, 2609, 2610, 2611, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 2620, 2621,
2622, 2623, 2624, 2625, 2626, 2627, 2628, 2629, 2630, 2631, 2632, 2633, 2634, 2635, 2636, 2637,
2638, 2639, 2640, 2641, 2642, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 2650, 2651, 2652, 2653,
2654, 2655, 2656, 2657, 2658, 2659, 2660, 2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669,
2670, 2671, 2672, 2673, 2674, 2675, 2676, 2677, 2678, 2679, 2680, 2681, 2682, 2683, 2684, 2685,
2686, 2687, 2688, 2689, 2690, 2691, 2692, 2693, 2694, 2695, 2696, 2697, 2698, 2699, 2700, 2701,
2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 2710, 2711, 2712, 2713, 2714
]
with open("nodes.txt", "w") as f:
s, dummy_base_nodes = gen_nodes(first_node_id=5487, query_nodes=nodes)
f.write(s)
s, dummy_movable_nodes = gen_nodes(first_node_id=5487+len(dummy_base_nodes), query_nodes=nodes)
f.write(s)
with open("boundaries.txt", "w") as f:
s = fix_base(dummy_base_nodes)
f.write(s)
s = constrain_dofs(dummy_movable_nodes)
f.write(s)
with open("equations.txt", "w") as f:
s = MPC(nodes, dummy_base_nodes, dummy_movable_nodes)
f.write(s)
So MPCs must suffice.