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Finite Element Code for Evaluation of In Situ Stiffness and In Situ Mass of Three-Dimensional Solids and Structures


        Equation Solution is ahead of research universities and institutes in evaluations of in situ stiffness and in situ mass in finite element method since 2004.

        Evaluation of in situ stiffness and in situ mass is important to non-destructive evaluation. Many universities and institutes have made researches into non-desctructive evaluation. Those researches are based on observations or experiments to propose criteria to, for example, detect a damage. Unlike those researches conducted at universities, the innovative method Equation Solution derived is completely under mathematical derivation. The derivation not only proves the convergence of in situ stiffness and in situ mass but also shows the first few lowest modes contribute most to in situ stiffness and in situ mass. The innovative method writes in situ stiffness and in situ mass in terms of cyclic frequency and partial ordinates of the first few modes.


        Stiffness and mass are two essential properties to analyze structural response. We have theoretical expression of stiffness and mass. However, those theoretical expression remains unchanged no matter how old a structure becomes, and cannot reflect the condition of actual structure. A structure condition could not remain unchanged after structure has been well constructed in position. We know material also could be deteriorated or aging, and structure may be damaged. Stiffness and mass of a structure vary all the time. The question we face today is how to determine the actual stiffness and mass ("in-situ stiffness and in situ mass") after structure has been well constructed in position. JUNE5 provides the answer.

        With in situ stiffness and in situ mass JUNE5 provides, for example,
  1. we can monitor structural health, and locate damages;
  2. we also can analyze, in advance, how a structure responds to a potential impact, and determine whether the structure has exceeded its useful life span;
  3. we also can evaluate, in advance, whether a structure is safe to a foreseen impact;
  4. we also can check if a structure is well repaired after a damage.
JUNE5 is an absolutely necessary tool to monitor structral health. It allows structural health to be evaluated at any time when necessary.


        Government agencies, for example, National Science Foundation, had awarded many grants to researches on non-destructive evaluations. It was unclear whether government-sponsored researches had developed a method to evaluate in situ stiffness and mass. Equation Solution had developed an innovative method.

        It is not a straightforward concept to evaluate in situ stiffness and mass. It is also impractical to directly evaluate in-situ stiffness or mass of a well-constructed structure. The difficulty to directly evaluate in-situ stiffness is similar to directly evaluate earth mass by a spring scale. That is impossible to build a spring scale big enough to hold the earth. Relevant physical property, i.e., gravitational force, indirectly estimates earth mass.

        Evaluation of in-situ stiffness has a difficulty similar to estimate earth mass, especially for large-scaled structures. We cannot directly measure in situ stiffness and mass. JUNE5 indirectly evaluates in-situ stiffness and in situ mass of a well-constructed structure by testing cyclic frequencies and partial ordinates of the first few modes.

        In order to apply partial ordinates of the first few modes, JUNE5 applies an unpublished method to condense a structure to the degrees of freedom where sensors monitor. The innovative condensation is different from traditional condensation (i.e., substructuring or Guyan condensation). The traditional technique applies Gaussian elimination or Guyan condensation to eliminate undesired unknowns. The traditional method has a big problem that the cyclic frequencies of condensed structure are not cyclic frequencies of the original structure. The original structure and the condensed structure may have the same static response, but have different dynamic responses, i.e., the condensed structure is not equivalent to the original structure.

        The condensation method applied in JUNE5 is innovative. The innovative method makes the condensed structure equivalent to the original structure. The original structure and condensed structure not only have the same static response but also have the same dynamic response. The cyclic frequences of the condensed structure are the first corresponding modes of the original structure. If we write this innovative condensation into algebraic equation, this innovative method leads to a new method that can condense an algebraic eigenvalue equation into a small system. For example, if we have a (5-by-5) algebraic eigenvalue equation

                    [A]{X} = s{X}

where s1, s2, s3, s4, and s5 are eigenvalues in increasing order. This innovative method can condense the (5-by-5) algebraic eigenvalue equation to a small system, for example, a (2-by-2) system

                    [B]{X} = t{X}

where t1 and t2 are eigenvalues. The most interesting result is that t1 and t2 are two of s1, s2, ..., and s5, and for our interest it also can be restricted that s1 = t1 and s2 = t2. Eigenvector of condensed system can be expanded to the original system.

        This innovative method that leads to condense algebraic eigenvalue equation was derived in 1996 by the originator of JUNE5. We had not heard a similar method to condense algebraic eigenvalue equation yet. JUNE5 is powered by the innovative condensation of algebraic eigenvalue equation. Because of equivalence, the condensed structure can represent the original structure. That allows us to apply limited sensors to evaluate a structure in any dimension. For example, we can monitor 8 ordinates of the first 10 modes to evaluate an in situ stiffness matrix of order 50000-by-50000. Certianly, more sensors produce a more accurate result.

        In-situ stiffness and mass matrices, evaluated by JUNE5, satisfy structural properties.
  1. If we apply in-situ stiffness and in situ mass to motion equation and solve the motion equation, the output, i.e., cyclic frequencies and ordinates of mode shapes, is equal to field test. There is no way for theoretical stiffness and mass to produce a result equal to field test. In situ stiffness and in situ mass reflect the actual condition of a well constructed structure.
  2. The output, mode shapes, is orthogonalized with respect to both in-situ stiffness and in-situ mass.
  3. In-situ stiffness and in-situ mass are dense and symmetric. Because of under the assumption of piecewise shape functions, theoretical expression of stiffness and mass is in a sparse matrix. We are not talking theoretical expression any more. In situ properties never have a piecewise assumption, and in situ stiffness and mass are dense in nature.

        The present release has the following elements:
  1. 2-node truss element
  2. 2-node frame element
  3. 4-node isotropic tetrahedron elements
  4. 6-node isotropic wedge elements
  5. 8-node isotropic brick elements
  6. 10-node isotropic tetrahedron elements
  7. 15-node isotropic wedge elemnts
  8. 20-node isotropic brick elements
For manual, click here.


        The following links can download the program.
  • Click here to download 32-bit executable for Windows.
  • Click here to download 64-bit executable for x86_64-linux.