FEATool Multiphysics
v1.17.0
Finite Element Analysis Toolbox
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EX_LINEARELASTICITY3 Parametric study for the bracket deflection model.
[ FEA, OUT ] = EX_LINEARELASTICITY3( VARARGIN ) Example to conduct parametric study of maximum stresses for the bracket deflection model.
Input Value/{Default} Description ----------------------------------------------------------------------------------- thickness [0.035 0.03 0.025 0.02] Plate thickness loads [1e4 2e4 1e5 1e6] Applied loads. . Output Value/(Size) Description ----------------------------------------------------------------------------------- fea struct Problem definition struct out struct Output struct
thickness = [ 0.035 0.03 0.025 0.02 ]; loads = [ 1e4 2e4 1e5 1e6 ]; %% Starting new model. fea.sdim = { 'x', 'y', 'z' }; fea = addphys( fea, @linearelasticity, { 'u', 'v', 'w' } ); for i=1:length(thickness) %% Geometry operations. fea.geom = struct; gobj = gobj_block( 0, 0.02, 0, 0.2, 0, 0.2, 'B1' ); fea = geom_add_gobj( fea, gobj ); gobj = gobj_block( 0, 0.2, 0, 0.2, 0.1-thickness(i)/2, 0.1+thickness(i)/2, 'B1' ); fea = geom_add_gobj( fea, gobj ); gobj = gobj_cylinder( [ 0.1, 0.1, 0.08 ], 0.08, 0.04, 3, 'C1' ); fea = geom_add_gobj( fea, gobj ); fea = geom_apply_formula( fea, 'B1+B2-C1' ); %% Grid operations. fea.grid = gridgen( fea, 'hmax', thickness(i)/2 ); for j=1:length(loads) %% Equation settings. fea.phys.el.dvar = { 'u', 'v', 'w' }; fea.phys.el.sfun = { 'sflag1', 'sflag1', 'sflag1' }; fea.phys.el.eqn.coef = { 'nu_el', 'nu', 'Poissons ratio', { '0.3' }; 'E_el', 'E', 'Modulus of elasticity', { '200e9' }; 'Fx_el', 'F_x', 'Body load in x-direction', { '0' }; 'Fy_el', 'F_y', 'Body load in y-direction', { '0' }; 'Fz_el', 'F_z', 'Body load in z-direction', { '0' }; 'u0_el', 'u0', 'Initial condition for u', { '0' }; 'v0_el', 'v0', 'Initial condition for v', { '0' }; 'w0_el', 'w0', 'Initial condition for w', { '0' } }; fea.phys.el.eqn.seqn = { 'u'' - ((E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*ux_x + (E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy_x + (E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz_x + (E_el/(1+nu_el)/2)*(uy_y+vx_y) + (E_el/(1+nu_el)/2)*(uz_z+wx_z)) = Fx_el', 'v'' - ((E_el/(1+nu_el)/2)*(uy_x+vx_x) + (E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux_y + (E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*vy_y + (E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz_y + (E_el/(1+nu_el)/2)*(vz_z+wy_z)) = Fy_el', 'w'' - ((E_el/(1+nu_el)/2)*(uz_x+wx_x) + (E_el/(1+nu_el)/2)*(vz_y+wy_y) + (E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux_z + (E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy_z + (E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*wz_z) = Fz_el' }; fea.phys.el.eqn.vars = { 'von Mieses stress', 'sqrt(((E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*ux+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz)^2+((E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux+(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*vy+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz)^2+((E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy+(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*wz)^2-((E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*ux+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz)*((E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux+(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*vy+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz)-((E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux+(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*vy+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz)*((E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy+(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*wz)-((E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*ux+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz)*((E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy+(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*wz)+3*((E_el/(1+nu_el)/2)*(uy+vx))^2+3*((E_el/(1+nu_el)/2)*(vz+wy))^2+3*((E_el/(1+nu_el)/2)*(uz+wx))^2)'; 'x-displacement', 'u'; 'y-displacement', 'v'; 'z-displacement', 'w'; 'Stress, x-component', '(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*ux+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz'; 'Stress, y-component', '(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux+(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*vy+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*wz'; 'Stress, z-component', '(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*ux+(E_el/((1+nu_el)*(1-2*nu_el))*nu_el)*vy+(E_el/((1+nu_el)*(1-2*nu_el))*(1-nu_el))*wz'; 'Stress, xy-component', '(E_el/(1+nu_el)/2)*(uy+vx)'; 'Stress, yz-component', '(E_el/(1+nu_el)/2)*(vz+wy)'; 'Stress, zx-component', '(E_el/(1+nu_el)/2)*(uz+wx)'; 'Displacement field', { 'u', 'v', 'w' } }; %% Constants and expressions. fea.expr = { 'load', loads(j) }; %% Boundary settings. n_bdr = max(fea.grid.b(3,:)); ind_fixed = findbdr( fea, 'x<0.005' ); ind_load = findbdr( fea, 'x>0.19' ); fea.phys.el.bdr.sel = ones(1,n_bdr); % Fix right boundary (set zero Dirichlet BCs). n_bdr = max(fea.grid.b(3,:)); % Number of boundaries. bctype = num2cell( zeros(3,n_bdr) ); % First set homogenous Neumann BCs everywhere. [bctype{:,ind_fixed}] = deal( 1 ); % Set Dirchlet BCs for right boundary. fea.phys.el.bdr.coef{1,5} = bctype; % Apply negative z-load to left outer boundary. bccoef = num2cell( zeros(3,n_bdr) ); [bccoef{3,ind_load}] = deal( '-load' ); fea.phys.el.bdr.coef{1,end} = bccoef; %% Solver call. fea = parsephys( fea ); fea = parseprob( fea ); fea.sol.u = solvestat( fea ); %% Postprocessing. s_vm = fea.phys.el.eqn.vars{1,2}; vm_stress = evalexpr( s_vm, fea.grid.p, fea ); max_vm_stress(i,j) = max(vm_stress); end end %% Visualization. [t,l] = meshgrid(thickness,loads); surf( t, l, max_vm_stress, log(max_vm_stress) ) xlabel('Thickness') ylabel('Load') zlabel('Maximum stress') view(45,30) out = max_vm_stress; if ( nargout==0 ) clear fea out end