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Non linear (geometric non linearity) problem- Programming shallow truss element-Reference book by Crisfield

I’m trying to program geometric non linear analysis (finite element)-for a shallow truss element.I am using the book by Crisfield for the purpose. Basically, I am using the incremental approach for analysis.And I am struck with a problem.The problem is that my Structural stiffness matrix (after application of Boundary conditions) is singular i.e. it’s determinant value is “0”. However, I am sure that my algorithm of assembly and application of boundary conditions is correct since the same algorithm works correctly for linear finite element analysis for which I have validated examples  My tangent stiffness matrix is the equation 2.23 of Crisfield’s book-I have attached the relevant portion of the same for your quick reference.Refer file named “Crisfield” My truss configuration is as shown in the document named “details” My questions are: 

  1. Does one have to apply transformation to equation 2.23 of Crisfield’s book?i.e. multiplication with transformation matrix cos theta_sin theta---etc?
  2. In my input I have defined Z1 and Z2 (As per Crisfield’s notation) as :

 For element 1: Z1 at node 1 : 0 ; Z2 at node 1:”X”For element 2: Z1 at node 1: 0  ; Z2 at node 1: “X” Whatever value I give for “X”, the structural stiffness matrix after the application of boundary conditions is singular. I have checked the element stiffness with hand alculations and is correct as the program output. Where I am going wrong?I am unable to make out—I think there is something wrong in input or I need to apply transformation which is not depicted in Crisfield’s book. Please please help    

AttachmentSize
PDF icon chapter 2 derivation.pdf110.58 KB
PDF icon truss details.pdf12.49 KB

please note that the rlevant portion of crisfields book is in the file named chapter 2 derivation.pdf and my truss configuration is as in file named truss details.pdf.please please help

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