# Linear Strain Triangle Mathematics: Stiffness, Stress and Consistent Load Vector

## Keywords:

consistent load vector for conical axe-symmetric shell element or pressure vessel element, modeling of multiple materials, mathematics of finite element LST, stiffness matrix, stress and, consistent load vector## Abstract

Typically, linear strain triangle LST is widely used for elastic analysis not only due to its ease but also due to the good results it can lead to over the traditional constant strain triangle CST. In plane elastic analysis of two combined materials the LST is quite reliable and trust worthy in terms of stress results for the same element size, LST is very useful in modelling combined materials thus believed to be efficient and can easily take into consideration, self-weight of used materials, strains due to causes other than loading; such as moisture, temperature, creep and shrinkage are easily incorporated. A mathematical formulation of stiffness matrix, stress and the more rarely dealt with consistent load vector for loads distributed on element edge are proved and highlighted for young engineers who mostly dealing with readily used FE codes, the formula proved for LST element load vector is further extended and thus a consisted load vector for conical axe-symmetric shell element is introduced.

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*American Scientific Research Journal for Engineering, Technology, and Sciences*,

*83*(1), 1–11. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/7074

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