By A. J. M. Ferreira
This ebook illustrates how MATLAB compact and strong programming framework could be very worthwhile within the finete point research of solids and constructions. The booklet almost immediately introduces finite aspect innovations and an intensive checklist of MATLAB codes for readers to take advantage of and alter. The ebook components diversity from extremely simple springs and bars to extra advanced beams and plates in static bending, unfastened vibrations and buckling problems.
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Additional resources for MATLAB Codes for Finite Element Analysis: Solids and Structures (Solid Mechanics and Its Applications)
5, in which the modulus of elasticity is E = 30e6, and the area of the cross-section is A = 1. m considers an isoparametric formulation. %................................................................ % MATLAB codes for Finite Element Analysis 38 3 Analysis of bars Fig. 0; % computation of the system stiffness matrix for e=1:numberElements; % elementDof: element degrees of freedom (Dof) elementDof=elementNodes(e,:) ; nn=length(elementDof); length_element=nodeCoordinates(elementDof(2))... 0); Xderivatives=naturalDerivatives*invJacobian; % B matrix B=zeros(1,nn); B(1:nn) = Xderivatives(:); stiffness(elementDof,elementDof)=...
0); Xderivatives=naturalDerivatives*invJacobian; % B matrix B=zeros(1,nn); B(1:nn) = Xderivatives(:); stiffness(elementDof,elementDof)=... stiffness(elementDof,elementDof)+B’*B*2*detJacobian*EA; end % boundary conditions and solution % prescribed dofs fixedDof=find(xx==min(nodeCoordinates(:)) ... | xx==max(nodeCoordinates(:)))’; prescribedDof=[fixedDof] % free Dof : activeDof activeDof=setdiff([1:numberNodes]’,[prescribedDof]); % solution GDof=numberNodes; displacements=solution(GDof,prescribedDof,stiffness,force); % output displacements/reactions outputDisplacementsReactions(displacements,stiffness,...
Then we deﬁne a vector containing all activeDof degrees of freedom, by setting up the diﬀerence between all degrees of freedom and the prescribed ones. The MATLAB function setdiff allows this operation. % boundary conditions and solution % prescribed dofs prescribedDof=[1;3;4]; % free Dof : activeDof activeDof=setdiff([1:numberNodes]’,[prescribedDof]); % solution displacements=stiffness(activeDof,activeDof)\force(activeDof); Note that the solution is performed with the active lines and columns only, by using a mask.
MATLAB Codes for Finite Element Analysis: Solids and Structures (Solid Mechanics and Its Applications) by A. J. M. Ferreira