Apply loads (demo_FEA_loads_static.cpp)
Tutorial that teaches how to use the FEA module to add loads to finite element models.
Loads are added via ChLoad objects.
There are various ready-to-use ChLoad objects, but here you can also learn how to define new ChLoad classes for custom loads.
Optionally the ChLoader classes can be used to automate some tasks, most noticeably the Gauss integration of distributed loads.
// =============================================================================
// PROJECT CHRONO - http://projectchrono.org
//
// Copyright (c) 2014 projectchrono.org
// All rights reserved.
//
// Use of this source code is governed by a BSD-style license that can be found
// in the LICENSE file at the top level of the distribution and at
// http://projectchrono.org/license-chrono.txt.
//
// =============================================================================
// Authors: Alessandro Tasora
// =============================================================================
//
// FEA demo on applying loads to beams, shells, volumes, etc.
//
// =============================================================================
#include "chrono/physics/ChLinkMate.h"
#include "chrono/physics/ChLoadContainer.h"
#include "chrono/physics/ChSystemSMC.h"
#include "chrono/solver/ChIterativeSolverLS.h"
#include "chrono/fea/ChElementBar.h"
#include "chrono/fea/ChElementBeamEuler.h"
#include "chrono/fea/ChElementHexaANCF_3813.h"
#include "chrono/fea/ChElementHexaCorot_20.h"
#include "chrono/fea/ChElementHexaCorot_8.h"
#include "chrono/fea/ChElementShellANCF_3423.h"
#include "chrono/fea/ChElementTetraCorot_10.h"
#include "chrono/fea/ChElementTetraCorot_4.h"
#include "chrono/fea/ChLinkDirFrame.h"
#include "chrono/fea/ChLinkPointFrame.h"
#include "chrono/fea/ChLinkPointFrame.h"
#include "chrono/fea/ChLoadsBeam.h"
#include "chrono/fea/ChMesh.h"
// Remember to use the namespace 'chrono' because all classes
// of Chrono::Engine belong to this namespace and its children...
using namespace chrono;
using namespace fea;
void test_1() {
GetLog() << "\n-------------------------------------------------\n";
GetLog() << "TEST: load applied to a beam \n\n";
// The physical system: it contains all physical objects.
ChSystemSMC my_system;
// Create a mesh:
auto my_mesh = chrono_types::make_shared<ChMesh>();
my_system.Add(my_mesh);
// Create some nodes.
// Default mass for FEM nodes is zero
mnodeA->SetMass(0.0);
mnodeB->SetMass(0.0);
my_mesh->AddNode(mnodeA);
my_mesh->AddNode(mnodeB);
// Create beam section & material
auto msection = chrono_types::make_shared<ChBeamSectionEulerAdvanced>();
double beam_wy = 0.1;
double beam_wz = 0.2;
msection->SetAsRectangularSection(beam_wy, beam_wz);
msection->SetYoungModulus(0.01e9);
msection->SetGshearModulus(0.01e9 * 0.3);
msection->SetBeamRaleyghDamping(0.200);
msection->SetDensity(1500);
// Create a beam of Eulero-Bernoulli type:
auto melementA = chrono_types::make_shared<ChElementBeamEuler>();
melementA->SetNodes(mnodeA, mnodeB);
melementA->SetSection(msection);
my_mesh->AddElement(melementA);
// Create also a truss
auto truss = chrono_types::make_shared<ChBody>();
truss->SetBodyFixed(true);
my_system.Add(truss);
// Create a constraint at the end of the beam
auto constr_a = chrono_types::make_shared<ChLinkMateGeneric>();
constr_a->Initialize(mnodeA, truss, false, mnodeA->Frame(), mnodeA->Frame());
my_system.Add(constr_a);
constr_a->SetConstrainedCoords(true, true, true, // x, y, z
true, true, true); // Rx, Ry, Rz
// APPLY SOME LOADS!
// First: loads must be added to "load containers",
// and load containers must be added to your system
auto mloadcontainer = chrono_types::make_shared<ChLoadContainer>();
my_system.Add(mloadcontainer);
// Example 1:
// Add a vertical load to the end of the beam element:
auto mwrench = chrono_types::make_shared<ChLoadBeamWrench>(melementA);
mwrench->loader.SetApplication(1.0); // in -1..+1 range, -1: end A, 0: mid, +1: end B
mwrench->loader.SetForce(ChVector<>(0, -0.2, 0));
mloadcontainer->Add(mwrench); // do not forget to add the load to the load container.
// Example 2:
// Add a distributed load along the beam element:
auto mwrenchdis = chrono_types::make_shared<ChLoadBeamWrenchDistributed>(melementA);
mwrenchdis->loader.SetForcePerUnit(ChVector<>(0, -0.1, 0)); // load per unit length
mloadcontainer->Add(mwrenchdis);
// Example 3:
// Add gravity (constant volumetric load)
auto mgravity = chrono_types::make_shared<ChLoad<ChLoaderGravity>>(melementA);
mloadcontainer->Add(mgravity);
// note that by default all solid elements in the mesh will already
// get gravitational force, if you want to bypass this automatic gravity, do:
my_mesh->SetAutomaticGravity(false);
// Example 4:
// Now, create a custom load for the beam element.
// There are some stubs in the ChLoaderU.h ChLoaderUV.h ChLoaderUVW.h headers,
// from which you can inherit. Here we inherit from
// For example, let's make a distributed triangular load. A load on the beam is a
// wrench, i.e. force+load per unit lenght applied at a certain abscissa U, that is a six-dimensional load.
// By the way, a triangular load will work as a constant one because a single Euler beam
// cannot feel more than this.
public:
// Useful: a constructor that also sets ChLoadable
MyLoaderTriangular(std::shared_ptr<ChLoadableU> mloadable) : ChLoaderUdistributed(mloadable){};
// Compute F=F(u)
// This is the function that you have to implement. It should return the
// load at U. For Eulero beams, loads are expected as 6-rows vectors, containing
// a wrench: forceX, forceY, forceZ, torqueX, torqueY, torqueZ.
virtual void ComputeF(
const double U,
ChVectorDynamic<>* state_x,
ChVectorDynamic<>* state_w
) {
double Fy_max = 0.005;
F.segment(3, 3).setZero(); // load, torque part
}
// Needed because inheriting ChLoaderUdistributed. Use 1 because linear load fx.
virtual int GetIntegrationPointsU() { return 1; }
};
// Create the load (and handle it with a shared pointer).
// The ChLoad is a 'container' for your ChLoader.
// It is created using templates, that is instancing a ChLoad<a_loader_class>()
std::shared_ptr<ChLoad<MyLoaderTriangular>> mloadtri(new ChLoad<MyLoaderTriangular>(melementA));
mloadcontainer->Add(mloadtri); // do not forget to add the load to the load container.
// Example 5:
// Create a custom load with stiff force, acting on a single node.
// As a stiff load, this will automatically generate a jacobian (tangent stiffness matrix K)
// that will be used in statics, implicit integrators, etc.
auto mnodeC = chrono_types::make_shared<ChNodeFEAxyz>(ChVector<>(2, 10, 3));
my_mesh->AddNode(mnodeC);
public:
MyLoaderPointStiff(std::shared_ptr<ChLoadableUVW> mloadable) : ChLoaderUVWatomic(mloadable, 0, 0, 0){};
// Compute F=F(u)
// This is the function that you have to implement. It should return the F load at U,V,W.
// For ChNodeFEAxyz, loads are expected as 3-rows vectors, containing F absolute force.
// As this is a stiff force field, dependency from state_x and state_y must be considered.
virtual void ComputeF(
const double U,
const double V,
const double W,
ChVectorDynamic<>* state_x,
ChVectorDynamic<>* state_w
) {
ChVector<> node_pos;
ChVector<> node_vel;
if (state_x) {
node_pos = state_x->segment(0, 3);
node_vel = state_w->segment(0, 3);
} else {
node_pos = std::dynamic_pointer_cast<ChNodeFEAxyz>(loadable)->GetPos();
node_vel = std::dynamic_pointer_cast<ChNodeFEAxyz>(loadable)->GetPos_dt();
}
// Just implement a simple force+spring+damper in xy plane,
// for spring&damper connected to absolute reference:
double Kx = 100;
double Ky = 400;
double Dx = 0.6;
double Dy = 0.9;
double x_offset = 2;
double y_offset = 10;
double x_force = 50;
double y_force = 0;
// Store the computed generalized forces in this->load_Q, same x,y,z order as in state_w
F(1) = y_force - Ky * (node_pos.y() - y_offset) - Dy * node_vel.y(); // Fy component of force
F(2) = 0; // Fz component of force
}
// Remember to set this as stiff, to enable the jacobians
virtual bool IsStiff() { return true; }
};
// Instance a ChLoad object, applying to a node, and passing a ChLoader as a template
// (in this case the ChLoader-inherited class is our MyLoaderPointStiff), and add to container:
std::shared_ptr<ChLoad<MyLoaderPointStiff>> mloadstiff(new ChLoad<MyLoaderPointStiff>(mnodeC));
mloadcontainer->Add(mloadstiff);
// Example 6:
// As before, create a custom load with stiff force, acting on a single node, but
// this time we inherit directly from ChLoadCustom, i.e. a load that does not require ChLoader features.
// This is mostly used in case one does not need the automatic surface/volume quadrature of ChLoader.
// As a stiff load, this will automatically generate a jacobian (tangent stiffness matrix K)
// that will be used in statics, implicit integrators, etc.
auto mnodeD = chrono_types::make_shared<ChNodeFEAxyz>(ChVector<>(2, 10, 3));
my_mesh->AddNode(mnodeD);
public:
MyLoadCustom(std::shared_ptr<ChLoadableUVW> mloadable) : ChLoadCustom(mloadable){};
virtual MyLoadCustom* Clone() const override { return new MyLoadCustom(*this); }
// Compute Q=Q(x,v)
// This is the function that you have to implement. It should return the generalized Q load
// (i.e.the force in generalized lagrangian coordinates).
// For ChNodeFEAxyz, Q loads are expected as 3-rows vectors, containing absolute force x,y,z.
// As this is a stiff force field, dependency from state_x and state_y must be considered.
ChStateDelta* state_w
) override {
ChVector<> node_pos;
ChVector<> node_vel;
if (state_x && state_w) {
node_pos = state_x->segment(0, 3);
node_vel = state_w->segment(0, 3);
} else {
node_pos = std::dynamic_pointer_cast<ChNodeFEAxyz>(loadable)->GetPos();
node_vel = std::dynamic_pointer_cast<ChNodeFEAxyz>(loadable)->GetPos_dt();
}
// Just implement a simple force+spring+damper in xy plane,
// for spring&damper connected to absolute reference:
double Kx = 100;
double Ky = 400;
double Dx = 0.6;
double Dy = 0.9;
double x_offset = 2;
double y_offset = 10;
double x_force = 50;
double y_force = 0;
// Store the computed generalized forces in this->load_Q, same x,y,z order as in state_w
this->load_Q(1) = y_force - Ky * (node_pos.y() - y_offset) - Dy * node_vel.y();
this->load_Q(2) = 0;
}
// OPTIONAL: if you want to provide an analytical jacobian, that might avoid the lengthy and approximate
// default numerical jacobian, just implement the following:
ChStateDelta* state_w,
ChMatrixRef mK,
ChMatrixRef mR,
ChMatrixRef mM
) override {
mK(0, 0) = 100;
mK(1, 1) = 400;
mR(0, 0) = 0.6;
mR(1, 1) = 0.9;
}
// Remember to set this as stiff, to enable the jacobians
virtual bool IsStiff() override { return true; }
};
// Instance load object, applying to a node, as in previous example, and add to container:
auto mloadcustom = chrono_types::make_shared<MyLoadCustom>(mnodeD);
mloadcontainer->Add(mloadcustom);
// Example 7:
// As before, create a custom load with stiff force, acting on MULTIPLE nodes at once.
// This time we will need the ChLoadCustomMultiple as base class.
// Those nodes (ie.e ChLoadable objects) can be added in my_mesh in whatever order,
// not necessarily contiguous, because the bookkeeping is automated.
// Being a stiff load, a jacobian will be automatically generated
// by default using numerical differentiation; but if you want you
// can override ComputeJacobian() and compute mK, mR analytically - see prev.example.
auto mnodeE = chrono_types::make_shared<ChNodeFEAxyz>(ChVector<>(2, 10, 3));
my_mesh->AddNode(mnodeE);
auto mnodeF = chrono_types::make_shared<ChNodeFEAxyz>(ChVector<>(2, 11, 3));
my_mesh->AddNode(mnodeF);
public:
MyLoadCustomMultiple(std::vector<std::shared_ptr<ChLoadable>>& mloadables) : ChLoadCustomMultiple(mloadables){};
virtual MyLoadCustomMultiple* Clone() const override { return new MyLoadCustomMultiple(*this); }
// Compute Q=Q(x,v)
// This is the function that you have to implement. It should return the generalized Q load
// (i.e.the force in generalized lagrangian coordinates).
// Since here we have multiple connected ChLoadable objects (the two nodes), the rule is that
// all the vectors (load_Q, state_x, state_w) are split in the same order that the loadable objects
// are added to MyLoadCustomMultiple; in this case for instance Q={Efx,Efy,Efz,Ffx,Ffy,Ffz}.
// As this is a stiff force field, dependency from state_x and state_y must be considered.
ChStateDelta* state_w
) override {
ChVector<> Enode_pos;
ChVector<> Enode_vel;
ChVector<> Fnode_pos;
ChVector<> Fnode_vel;
if (state_x && state_w) {
Enode_pos = state_x->segment(0, 3);
Enode_vel = state_w->segment(0, 3);
Fnode_pos = state_x->segment(3, 3);
Fnode_vel = state_w->segment(3, 3);
} else {
// explicit integrators might call ComputeQ(0,0), null pointers mean
// that we assume current state, without passing state_x for efficiency
Enode_pos = std::dynamic_pointer_cast<ChNodeFEAxyz>(loadables[0])->GetPos();
Enode_vel = std::dynamic_pointer_cast<ChNodeFEAxyz>(loadables[0])->GetPos_dt();
Fnode_pos = std::dynamic_pointer_cast<ChNodeFEAxyz>(loadables[1])->GetPos();
Fnode_vel = std::dynamic_pointer_cast<ChNodeFEAxyz>(loadables[1])->GetPos_dt();
}
// Just implement two simple force+spring+dampers in xy plane:
// ... from node E to ground,
double Kx1 = 60;
double Ky1 = 50;
double Dx1 = 0.3;
double Dy1 = 0.2;
double E_x_offset = 2;
double E_y_offset = 10;
-Ky1 * (Enode_pos.y() - E_y_offset) - Dy1 * Enode_vel.y(), 0);
// ... from node F to node E,
double Ky2 = 10;
double Dy2 = 0.2;
double EF_dist = 1;
ChVector<> spring2(
0, -Ky2 * (Fnode_pos.y() - Enode_pos.y() - EF_dist) - Dy2 * (Enode_vel.y() - Fnode_vel.y()), 0);
double Fforcey = 2;
// store generalized forces as a contiguous vector in this->load_Q, with same order of state_w
this->load_Q(0) = spring1.x() - spring2.x(); // Fx component of force on 1st node
this->load_Q(1) = spring1.y() - spring2.y(); // Fy component of force on 1st node
this->load_Q(2) = spring1.z() - spring2.z(); // Fz component of force on 1st node
this->load_Q(3) = spring2.x(); // Fx component of force on 2nd node
this->load_Q(4) = spring2.y() + Fforcey; // Fy component of force on 2nd node
this->load_Q(5) = spring2.z(); // Fz component of force on 2nd node
}
// OPTIONAL: if you want to provide an analytical jacobian, just implement the following:
// virtual void ComputeJacobian(...)
// Remember to set this as stiff, to enable the jacobians
virtual bool IsStiff() override { return true; }
};
// Instance load object. This require a list of ChLoadable objects
// (these are our two nodes,pay attention to the sequence order), and add to container.
std::vector<std::shared_ptr<ChLoadable>> mnodelist;
mnodelist.push_back(mnodeE);
mnodelist.push_back(mnodeF);
auto mloadcustommultiple = chrono_types::make_shared<MyLoadCustomMultiple>(mnodelist);
mloadcontainer->Add(mloadcustommultiple);
// Setup a MINRES solver. For FEA one cannot use the default PSOR type solver.
auto solver = chrono_types::make_shared<ChSolverMINRES>();
my_system.SetSolver(solver);
solver->SetMaxIterations(100);
solver->SetTolerance(1e-10);
solver->EnableDiagonalPreconditioner(true);
solver->SetVerbose(true);
// Perform a static analysis:
my_system.DoStaticLinear();
}
int main(int argc, char* argv[]) {
test_1();
return 0;
}
void Add(std::shared_ptr< ChPhysicsItem > item)
Attach an arbitrary ChPhysicsItem (e.g.
Definition: ChSystem.cpp:170
ChLog & GetLog()
Global function to get the current ChLog object.
Definition: ChLog.cpp:39
bool DoStaticLinear()
Solve the position of static equilibrium (and the reactions).
Definition: ChSystem.cpp:1516
Eigen::Ref< Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > > ChMatrixRef
Reference to a dense matrix expression, with double coefficients.
Definition: ChMatrix.h:112
Eigen::Map< Eigen::Matrix< Real, 3, 1 > > eigen()
View this 3d vector as an Eigen vector.
Definition: ChVector.h:72
Class of loaders for ChLoadableUVW objects (which support volume loads) of atomic type,...
Definition: ChLoaderUVW.h:153
Definition of general purpose 3d vector variables, such as points in 3D.
Definition: ChVector.h:35
Class for a physical system in which contact is modeled using a smooth (penalty-based) method.
Definition: ChSystemSMC.h:31
virtual void SetSolver(std::shared_ptr< ChSolver > newsolver)
Attach a solver (derived from ChSolver) for use by this system.
Definition: ChSystem.cpp:307
Class for a load acting on a single ChLoadable item, via ChLoader objects.
Definition: ChLoad.h:149
Eigen::Matrix< T, Eigen::Dynamic, 1, Eigen::ColMajor > ChVectorDynamic
Column vector with dynamic size (i.e., with size a run-time variable, unknown at compile time).
Definition: ChMatrix.h:88
Class of loaders for ChLoadableU objects (which support line loads), for loads of distributed type,...
Definition: ChLoaderU.h:47
Class for incremental form of state of time-integrable objects.
Definition: ChState.h:125
