truss.hh

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// SPDX-FileCopyrightText: 2021-2024 The Ikarus Developers mueller@ibb.uni-stuttgart.de
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
 
#include <optional>
 
#include <dune/localfefunctions/eigenDuneTransformations.hh>
 
#include <ikarus/finiteelements/fehelper.hh>
#include <ikarus/finiteelements/ferequirements.hh>
 
namespace Ikarus {
 
template <typename PreFE, typename FE>
class Truss;
 
struct TrussPre
{
  double E; // Young's modulus
  double A; // Cross-section area
 
  template <typename PreFE, typename FE>
  using Skill = Truss<PreFE, FE>;
};
 
template <typename PreFE, typename FE>
class Truss
    : public ResultTypeBase<ResultTypes::cauchyAxialForce, ResultTypes::PK2AxialForce, ResultTypes::linearAxialForce>
{
public:
  using Traits       = PreFE::Traits;
  using BasisHandler = typename Traits::BasisHandler;
  using FlatBasis    = typename Traits::FlatBasis;
  using Requirement =
      FERequirementsFactory<FESolutions::displacement, FEParameter::loadfactor, Traits::useEigenRef>::type;
  using LocalView = typename Traits::LocalView;
  using Geometry  = typename Traits::Geometry;
  using GridView  = typename Traits::GridView;
  using Element   = typename Traits::Element;
  using Pre       = TrussPre;
 
  static constexpr int myDim    = Traits::mydim;
  static constexpr int worldDim = Traits::worlddim;
  static_assert(myDim == 1, "Truss elements should have myDim == 1");
 
  template <typename ST>
  struct KinematicVariables
  {
    double L;                  
    ST l;                      
    ST Elin;                   
    ST Egl;                    
    Eigen::VectorX<ST> dEdu;   
    Eigen::MatrixX<ST> ddEddu; 
  };
 
  explicit Truss(const Pre& pre)
      : E{pre.E},
        A{pre.A} {}
 
  template <typename ST = double>
  auto displacement(const Requirement& par,
                    const std::optional<std::reference_wrapper<const Eigen::VectorX<ST>>>& dx = std::nullopt) const {
    const auto& d = par.globalSolution();
    auto disp     = Ikarus::FEHelper::localSolutionBlockVector<Traits>(d, underlying().localView(), dx);
    return disp;
  }
 
  template <class ST = double>
  KinematicVariables<ST> computeStrain(
      const Requirement& par,
      const std::optional<std::reference_wrapper<const Eigen::VectorX<ST>>>& dx = std::nullopt) const {
    KinematicVariables<ST> kin;
    const auto& localView    = underlying().localView();
    const auto& tree         = localView.tree();
    const auto numberOfNodes = tree.child(0).finiteElement().size();
    auto& ele                = localView.element();
    const auto X1            = Dune::toEigen(ele.geometry().corner(0));
    const auto X2            = Dune::toEigen(ele.geometry().corner(1));
    const auto u             = Dune::viewAsEigenMatrixAsDynFixed(displacement(par, dx)).transpose().eval();
    const auto A1            = X2 - X1;
    const auto ud1           = u.col(1) - u.col(0);
 
    const Eigen::Vector<ST, worldDim> x1 = X1 + u.col(0);
    const Eigen::Vector<ST, worldDim> x2 = X2 + u.col(1);
 
    const double Lsquared = A1.squaredNorm();
    const ST lsquared     = (x2 - x1).squaredNorm();
 
    kin.L = sqrt(Lsquared);
    kin.l = sqrt(lsquared);
 
    // Linear strain
    kin.Elin = (kin.l - kin.L) / kin.L;
 
    // Green-Lagrange strains
    kin.Egl = 0.5 * (lsquared - Lsquared) / Lsquared;
 
    // First derivative of Egl w.r.t displacements
    kin.dEdu.setZero(worldDim * numberOfNodes);
    kin.dEdu << -A1 - ud1, A1 + ud1;
    kin.dEdu /= Lsquared;
 
    // Second derivative of Egl w.r.t displacements
    kin.ddEddu.setIdentity(worldDim * numberOfNodes, worldDim * numberOfNodes);
    kin.ddEddu.template topRightCorner<worldDim, worldDim>()   = -Eigen::Matrix<ST, worldDim, worldDim>::Identity();
    kin.ddEddu.template bottomLeftCorner<worldDim, worldDim>() = -Eigen::Matrix<ST, worldDim, worldDim>::Identity();
    kin.ddEddu /= Lsquared;
 
    return kin;
  }
 
public:
  template <template <typename, int, int> class RT>
  requires(supportsResultType<RT>())
  auto calculateAtImpl(const Requirement& req, [[maybe_unused]] const Dune::FieldVector<double, Traits::mydim>& local,
                       Dune::PriorityTag<0>) const {
    using RTWrapper                            = ResultWrapper<RT<double, myDim, myDim>, ResultShape::Vector>;
    const auto [L, l, Elin, Egl, dEdu, ddEddu] = computeStrain(req);
    if constexpr (isSameResultType<RT, ResultTypes::cauchyAxialForce>) {
      auto N = Eigen::Vector<double, 1>{E * A * Egl * l / L}; // Axial force in deformed configuration
      return RTWrapper{N};
    }
    if constexpr (isSameResultType<RT, ResultTypes::PK2AxialForce>) {
      auto N = Eigen::Vector<double, 1>{E * A * Egl}; // Axial force in undeformed configuration
      return RTWrapper{N};
    }
    if constexpr (isSameResultType<RT, ResultTypes::linearAxialForce>) {
      auto N = Eigen::Vector<double, 1>{E * A * Elin};
      return RTWrapper{N};
    }
  }
 
private:
  //> CRTP
  const auto& underlying() const { return static_cast<const FE&>(*this); }
  auto& underlying() { return static_cast<FE&>(*this); }
 
  double E;
  double A;
 
protected:
  template <typename ScalarType>
  void calculateMatrixImpl(
      const Requirement& par, const MatrixAffordance& affordance, typename Traits::template MatrixType<> K,
      const std::optional<std::reference_wrapper<const Eigen::VectorX<ScalarType>>>& dx = std::nullopt) const {
    const auto [L, l, Elin, Egl, dEdu, ddEddu] = computeStrain(par, dx);
    K += E * A * L * (dEdu * dEdu.transpose() + ddEddu * Egl);
  }
 
  template <typename ScalarType>
  auto calculateScalarImpl(const Requirement& par, ScalarAffordance affordance,
                           const std::optional<std::reference_wrapper<const Eigen::VectorX<ScalarType>>>& dx =
                               std::nullopt) const -> ScalarType {
    const auto [L, l, Elin, Egl, dEdu, ddEddu] = computeStrain(par, dx);
    return 0.5 * E * A * L * Egl * Egl;
  }
 
  template <typename ScalarType>
  void calculateVectorImpl(
      const Requirement& par, VectorAffordance affordance, typename Traits::template VectorType<ScalarType> force,
      const std::optional<std::reference_wrapper<const Eigen::VectorX<ScalarType>>>& dx = std::nullopt) const {
    const auto [L, l, Elin, Egl, dEdu, ddEddu] = computeStrain(par, dx);
    force += E * A * Egl * L * dEdu;
  }
};
 
inline auto truss(const double E, const double A) {
  TrussPre pre(E, A);
 
  return pre;
}
} // namespace Ikarus