NonLinearDynamicMultibody

class sharpy.solvers.nonlineardynamicmultibody.NonLinearDynamicMultibody

Nonlinear dynamic multibody

Nonlinear dynamic step solver for multibody structures.

The settings that this solver accepts are given by a dictionary, with the following key-value pairs:

Name	Type	Description	Default
print_info	bool	Print output to screen	True
max_iterations	int	Sets maximum number of iterations	100
num_load_steps	int		1
delta_curved	float		0.01
min_delta	float	Structural solver tolerance	1e-05
newmark_damp	float	Sets the Newmark damping coefficient	0.0001
gravity_on	bool	Flag to include gravitational forces	False
gravity	float	Gravitational acceleration	9.81
gravity_dir	list(float)	Direction in G where gravity applies	[0.0, 0.0, 1.0]
relaxation_factor	float		0.3
dt	float	Time step increment	0.01
num_steps	int		500
time_integrator	str	Method to perform time integration	NewmarkBeta
time_integrator_settings	dict	Settings for the time integrator	{}
write_lm	bool	Write lagrange multipliers	False
relax_factor_lm	float	Relaxation factor for Lagrange Multipliers. 0 no relaxation. 1 full relaxation	0.0

assembly_MB_eq_system(MB_beam, MB_tstep, ts, dt, Lambda, Lambda_dot, MBdict)

This function generates the matrix and vector associated to the linear system to solve a structural iteration It usses a Newmark-beta scheme for time integration. Being M, C and K the mass, damping and stiffness matrices of the system:

\[MB_Asys = MB_K + MB_C\]

rac{gamma}{eta dt} + rac{1}{eta dt^2} MB_M

Args:

MB_beam (list(Beam)): each entry represents a body MB_tstep (list(StructTimeStepInfo)): each entry represents a body ts (int): Time step number dt(int): time step Lambda (np.ndarray): Lagrange Multipliers array Lambda_dot (np.ndarray): Time derivarive of Lambda MBdict (dict): Dictionary including the multibody information

Returns:

MB_Asys (np.ndarray): Matrix of the systems of equations MB_Q (np.ndarray): Vector of the systems of equations

compute_forces_constraints(MB_beam, MB_tstep, ts, dt, Lambda, Lambda_dot)

This function computes the forces generated at Lagrange Constraints

Parameters

• MB_beam (list(Beam)) – each entry represents a body

• MB_tstep (list(StructTimeStepInfo)) – each entry represents a body

• ts (int) – Time step number

• dt (float) – Time step increment

• Lambda (np.ndarray) – Lagrange Multipliers array

• Lambda_dot (np.ndarray) – Time derivarive of Lambda

Warning

This function is underdevelopment and not fully functional

define_sys_size()

This function defines the number of degrees of freedom in a multibody systems

Each body contributes with num_dof degrees of freedom and 10 more if the associated local FoR can move or has Lagrange Constraints associated

integrate_position(MB_beam, MB_tstep, dt)

This function integrates the position of each local A FoR after the structural iteration has been solved.

It uses a Newmark-beta approximation.

Parameters

• MB_beam (list(Beam)) – each entry represents a body

• MB_tstep (list(StructTimeStepInfo)) – each entry represents a body

• dt (int) – time step