Preface |
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xi | |
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1 | (8) |
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The concept of a flexible multibody system |
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1 | (5) |
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6 | (3) |
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Generalized Coordinates for Mechanism Analysis |
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9 | (30) |
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The four-bar mechanism example |
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10 | (1) |
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Description in terms of minimal coordinates |
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11 | (2) |
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Description in terms of Lagrangian coordinates |
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13 | (4) |
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Hartenberg-Denavit method |
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14 | (3) |
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Description in terms of Cartesian coordinates |
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17 | (1) |
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Description in terms of finite element coordinates |
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18 | (8) |
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Strong form of kinematic constraints for kinematic analysis |
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18 | (2) |
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The zero strain energy approach |
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20 | (1) |
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Numerical solution of the kinematic problem |
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21 | (2) |
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Generalization to statics |
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23 | (1) |
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Generalization to dynamics |
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24 | (2) |
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Example: kinematics of deployment of solar array |
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26 | (3) |
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Time integration of equations of motion |
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29 | (4) |
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Example: the double pendulum |
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33 | (6) |
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Kinematics of Finite Motion |
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39 | (28) |
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Matrix representation of vector operations |
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40 | (4) |
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Kinematic description of rigid body motion |
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44 | (11) |
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44 | (4) |
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Non-commutative character of finite rotations |
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48 | (1) |
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Explicit expressions of the rotation operator |
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49 | (3) |
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General motion of a rigid body |
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52 | (3) |
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Velocity analysis of rigid motion |
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55 | (5) |
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Velocity analysis of spherical motion |
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55 | (1) |
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Explicit expression of the angular velocities |
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56 | (2) |
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Velocity analysis of arbitrary body motion. Instantaneous screw axis |
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58 | (2) |
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Acceleration analysis of rigid motion |
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60 | (2) |
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Acceleration analysis of spherical motion |
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60 | (1) |
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Explicit expression of angular accelerations |
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61 | (1) |
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Time rate of change of instantaneous rotation axis |
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61 | (1) |
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Infinitesimal spherical motion and rotation increments |
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62 | (5) |
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Spatial and material infinitesimal rotations |
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62 | (1) |
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Variation of angular velocities |
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63 | (1) |
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Angular velocities and accelerations in a moving frame |
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64 | (1) |
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Incremental rotations as unknowns |
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65 | (2) |
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Parameterization of Spherical Motion |
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67 | (22) |
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Parameterization of rigid body spherical motion |
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69 | (1) |
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The Cartesian rotation vector |
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69 | (2) |
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Cayley form of rotation matrix ---Rodrigues parameters |
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71 | (2) |
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Finite rotations in terms of Euler parameters |
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73 | (3) |
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Quaternion algebra and finite rotations |
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76 | (5) |
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The Conformal Rotation Vector (CRV) |
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81 | (2) |
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83 | (1) |
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Geometric description of finite rotations |
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84 | (5) |
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84 | (2) |
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86 | (3) |
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89 | (16) |
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89 | (1) |
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90 | (2) |
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92 | (1) |
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Equations of motion in standard form |
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93 | (2) |
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Equations of motion in parameterized form |
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95 | (2) |
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Incremental form of the motion equations |
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97 | (3) |
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Exact linearization at equilibrium |
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100 | (1) |
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Example: top motion in a gravity field |
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101 | (4) |
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105 | (34) |
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107 | (1) |
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The displacement gradient measure of deformation |
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108 | (2) |
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Pseudo-polar decomposition of the Jacobian matrix |
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110 | (1) |
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111 | (2) |
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Local form of equilibrium |
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113 | (4) |
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Variation of beam strains |
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117 | (3) |
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Weak form of beam equations |
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118 | (1) |
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119 | (1) |
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Displacement finite element modelling |
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120 | (7) |
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120 | (1) |
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Construction of the beam strain matrix |
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120 | (1) |
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Discretized form of the dynamic equilibrium equations |
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121 | (1) |
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Linearization of dynamic equilibrium equations |
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122 | (5) |
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Shear locking and reduced integration |
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127 | (4) |
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131 | (8) |
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Cantilever beam: effect of residual bending flexibility correction |
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131 | (1) |
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Cantilever beam with two transverse loads |
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132 | (1) |
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Cantilever 45-degree bend |
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133 | (1) |
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134 | (1) |
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Clamped-hinged circular arch |
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135 | (1) |
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Out of plane buckling of a right-angle frame |
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136 | (3) |
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System Constraints: Modelling of Joints |
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139 | (46) |
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Types of constraints encountered in kinematic analysis |
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140 | (2) |
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Numerical solution of constrained algebraic problems |
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142 | (4) |
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The constraint elimination method |
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143 | (1) |
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The Lagrange multiplier method |
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144 | (1) |
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The penalty function method |
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144 | (1) |
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The augmented Lagrangian method |
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145 | (1) |
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The perturbed Lagrangian method |
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146 | (1) |
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Unconstrained dynamic problems |
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146 | (1) |
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Constrained dynamic problems |
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147 | (3) |
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The case of holonomic constraints |
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147 | (2) |
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The case of nonholonomic constraints |
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149 | (1) |
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Classification of kinematic pairs |
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150 | (2) |
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150 | (2) |
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152 | (1) |
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Modelling of lower-pair joints |
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152 | (5) |
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Formulation of the hinge joint |
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153 | (2) |
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155 | (2) |
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Other infinitely rigid lower pairs |
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157 | (3) |
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157 | (1) |
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158 | (1) |
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159 | (1) |
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160 | (1) |
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160 | (1) |
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Modelling of some higher-pair joints |
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160 | (7) |
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160 | (1) |
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161 | (1) |
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162 | (1) |
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163 | (3) |
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166 | (1) |
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Flexible effects in joints |
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167 | (7) |
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167 | (2) |
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169 | (2) |
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171 | (3) |
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Interference between links |
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174 | (2) |
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Example: retraction of a three-longeron truss |
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176 | (6) |
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182 | (3) |
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Substructuring Techniques |
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185 | (34) |
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Concept of mechanical impedance |
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187 | (4) |
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The Craig---Bampton method |
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191 | (1) |
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Mechanical admittance for discrete systems |
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192 | (3) |
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Restricted admittance: Mac Neal and Rubin methods |
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195 | (3) |
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197 | (1) |
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197 | (1) |
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Nonlinear description of a superelement |
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198 | (5) |
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Computation of the weight coefficients α |
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202 | (1) |
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Computation of the strain energy |
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203 | (1) |
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Corotational evaluation of the kinetic energy |
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204 | (4) |
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Variation of kinetic energy and inertia forces |
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206 | (1) |
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Tangent mass and pseudo damping matrices |
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207 | (1) |
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208 | (11) |
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208 | (4) |
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Beam on a spherical joint |
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212 | (1) |
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Deployment of the MEA antenna |
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213 | (6) |
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Static and Kinematic Analyses of Multibody Systems |
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219 | (44) |
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221 | (1) |
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Tracing the equilibrium path in structural analysis |
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222 | (3) |
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Selection of an appropriate metric |
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225 | (2) |
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Scheme to advance the solution |
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227 | (4) |
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227 | (2) |
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229 | (2) |
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Remarks on implementation aspects |
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231 | (2) |
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Formulation of flexible mechanisms problems |
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233 | (1) |
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234 | (7) |
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Three pinned-bar structure |
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235 | (1) |
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236 | (2) |
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238 | (1) |
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Buckling of a two hinged beam structure with axial load |
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239 | (2) |
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Singular points detection along the equilibrium path |
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241 | (3) |
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Solution of the system of equations |
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243 | (1) |
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Terms involving derivatives of the tangent matrix |
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244 | (1) |
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Null eigenvector updating under change of reference |
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245 | (3) |
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Null eigenvector updating in beam models |
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247 | (1) |
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Computation of the path tangents at a singular point |
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248 | (2) |
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250 | (9) |
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Rigid bar/springs mechanism |
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250 | (2) |
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252 | (2) |
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254 | (3) |
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Deep circular arch under vertical load |
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257 | (2) |
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259 | (4) |
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Time Integration of Constrained Systems |
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263 | (22) |
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Solution of dynamic constrained systems |
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265 | (4) |
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Constraint regularization |
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266 | (1) |
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266 | (1) |
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267 | (2) |
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Equations of motion of constrained dynamic systems |
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269 | (2) |
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271 | (4) |
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275 | (2) |
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Stability of time integration methods for DAE systems |
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277 | (4) |
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The Newmark method without numerical dissipation |
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279 | (1) |
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The Newmark method with numerical dissipation |
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280 | (1) |
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The Hilber---Hughes---Taylor algorithm |
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281 | (1) |
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281 | (1) |
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Example: the double pendulum |
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281 | (4) |
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Automatic Step Size Control |
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285 | (18) |
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Local truncation error estimation |
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286 | (1) |
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Local error analysis for the SDOF oscillator |
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287 | (2) |
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287 | (1) |
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Expected value of the non-dimensional error |
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288 | (1) |
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Time integration strategy |
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289 | (1) |
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Local error analysis of uncoupled MDOF systems |
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289 | (3) |
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289 | (1) |
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Expected value of the non-dimensional error |
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290 | (1) |
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Time integration strategy |
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290 | (2) |
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Local error analysis of coupled MDOF systems |
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292 | (3) |
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Projection on a modal basis |
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292 | (1) |
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Bounds on the modal displacement amplitudes |
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292 | (1) |
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Time integration strategy |
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293 | (2) |
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Strategy for changing the time step |
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295 | (1) |
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296 | (4) |
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296 | (1) |
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Articulated beams with locking mechanism |
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297 | (2) |
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Double pendulum with impulsive behaviour |
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299 | (1) |
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300 | (3) |
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Energy Conserving Time Integration |
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303 | (14) |
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General formulation of a multibody dynamics problem |
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304 | (2) |
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Time discretization by the mid-point rule |
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306 | (1) |
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307 | (1) |
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Application to top motion |
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308 | (4) |
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Rotation parameterization |
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309 | (2) |
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311 | (1) |
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The case of elastic systems |
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312 | (4) |
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Energy conservation and internal force averaging |
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315 | (1) |
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316 | (1) |
References |
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317 | (8) |
Index |
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325 | |