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Using volume integral( dx dy dz) to do a Analytical Engineering Analysis of 3D Shapes without using mesh based FEA. Like integration calculates area under curve and FEA do a filled rectangular mesh or cubic mesh approximation of shapes for engineering analysis here propose modified volume integral method to Analytical Engineering Analysis of 3D Shapes. Volume integral is where ∆x, ∆y, ∆z tends to zero. The difference between regular volume integral is that the function should change after each integration of volume integration ( 3 steps of integration). For example,.

Required continuous smooth function of stress or heat in a 3D solid shape

The boundary conditions are given as limits (u(x), u(y), u(z) .. v(x), v(y), v(z) )of integration

This is a new engineering analysis where a continuous plot of result is made; unlike FEA, where discrete results are made that depends on size or number of elements. this will revolutionize engineering analysis where the results of engineering analysis are like a vector image rather than raster image

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