Added capability for lumped inertia properties in the platform

The user can now specify points with inertial properties (mass and moments of inertia) that are added to the total inertia of the floating platform. This is particularly useful for cases where we only have the total mass and moments of inertia of the platform.

Added the relevant section (commented out) in `examples/VolturnUS-S _example.yaml` to exemplify the usage of this new capability.

New test case `VolturnUS-S-pointInertia.yaml`, which is run in`test_fowt.py` and in `test_model.py`

Author: lucas-carmo

examples/VolturnUS-S_example.yaml

@@ -1092,6 +1092,14 @@ platform:
     dlsMax       :  5.0     # maximum node splitting section amount for platform members; can't be 0
     qtfPath      :  'IEA-15-240-RWT-UMaineSemi.12d'      # path to the qtf file for the platform
 
+    # # `pointInertias` in as optional input that allows the user to specify lumped inertial properties
+    # # of the platform in addition (or instead of) the distributed inertia properties of each member.
+    # pointInertias: # List of lumped inertial properties
+    #  - name : point1
+    #    mass : 1.7754e+7 # [kg]
+    #    moments_of_inertia: [1.251E+10, 1.251E+10, 2.367E+10, 0, 0, 0] # Jxx, Jyy, Jzz, Jxy, Jxz, Jyz [kg*m^2]
+    #    location : [0, 0, -14.94] # 
+
     members:   # list all members here
 
       - name      :  center_column             # [-]    an identifier (no longer has to be number)       

raft/raft_fowt.py

@@ -56,7 +56,24 @@ def __init__(self, design, w, mpb, depth=600, x_ref=0, y_ref=0, heading_adjust=0
         self.x_ref = x_ref      # reference x position of the FOWT in the array [m]
         self.y_ref = y_ref      # reference y position of the FOWT in the array [m]
         self.r6 = np.zeros(6)   # mean position/orientation in absolute/array coordinates [m,rad]
-        
+
+        # Platform lumped inertias
+        self.pointInertias = []        
+        if 'pointInertias' in design['platform']:
+            nPoints = len(design['platform']['pointInertias'])            
+            for ip, pointInertia in enumerate(design['platform']['pointInertias']):
+                self.pointInertias.append({'m': 0, 'inertia': np.zeros([6, 6]), 'r': np.zeros([3,])}) # mass, inertia, and position of each point mass to be added to the platform
+                pointMass = getFromDict(pointInertia, 'mass', shape=0, default=0) # mass of the substructure [kg]
+                self.pointInertias[-1]['m'] = pointMass
+                auxInertia = getFromDict(pointInertia, 'moments_of_inertia', shape=6, default=[0,0,0]) # moments of inertia of the substructure [kg*m^2] - specified in the order Jxx, Jyy, Jzz, Jxy, Jxz, Jyz
+                self.pointInertias[-1]['inertia'] = np.array([[pointMass, 0, 0, 0, 0, 0],
+                                                              [0, pointMass, 0, 0, 0, 0],
+                                                              [0, 0, pointMass, 0, 0, 0],
+                                                              [0, 0, 0, auxInertia[0], auxInertia[3], auxInertia[4]],
+                                                              [0, 0, 0, auxInertia[3], auxInertia[1], auxInertia[5]],
+                                                              [0, 0, 0, auxInertia[4], auxInertia[5], auxInertia[2]]])
+                self.pointInertias[-1]['r'] = getFromDict(pointInertia, 'location', shape=3, default=[0,0,0])
+                        
         # count number of platform members
         self.nplatmems = 0
         for platmem in design['platform']['members']:
@@ -479,6 +496,18 @@ def calcStatics(self):
             self.M_struc += translateMatrix6to6DOF(Mmat, rotor.r_CG_rel)                            # mass/inertia matrix
             m_center_sum += rotor.r_CG_rel*rotor.mRNA
 
+
+        # ------------------------- include point inertia properties -----------------------------
+        for ip, pointInertia in enumerate(self.pointInertias):            
+            self.M_struc += translateMatrix6to6DOF(pointInertia['inertia'], pointInertia['r'])
+            self.W_struc += translateForce3to6DOF( np.array([0,0, -g*pointInertia['m']]), pointInertia['r'] )
+            m_center_sum += pointInertia['r']*pointInertia['m']
+
+            self.m_sub += pointInertia['m']
+            self.M_struc_sub += translateMatrix6to6DOF(pointInertia['inertia'], pointInertia['r'])     # mass matrix of the substructure about the PRP
+            m_sub_sum += pointInertia['r']*pointInertia['m']        # product sum of the substructure members and their centers of mass [kg-m]
+
+
         # ----------- process inertia-related totals ----------------
 
         m_all = self.M_struc[0,0]             # total mass of all the members

raft/raft_member.py

@@ -103,7 +103,7 @@ def __init__(self, mi, nw, BEM=[], heading=0):
                 self.MCF = False
 
 
-        self.t         = getFromDict(mi, 't', shape=n)               # shell thickness at each station [m]
+        self.t         = getFromDict(mi, 't', shape=n, default=0)  # shell thickness at each station [m]
         self.rho_shell = getFromDict(mi, 'rho_shell', shape=0, default=8500.) # shell mass density [kg/m^3]
 
 
@@ -707,7 +707,7 @@ def RectangularFrustumMOI(La, Wa, Lb, Wb, H, p):
         self.mshell = mshell
         self.mfill  = mfill
         mass = self.M_struc[0,0]        # total mass of the entire member [kg]
-        center = mass_center/mass       # total center of mass of the entire member from the PRP [m]
+        center = mass_center/mass if mass!=0 else np.array([0,0,0])       # total center of mass of the entire member from the PRP [m]
 
 
         return mass, center, mshell, mfill, pfill