Abstract: For each (ij)-th tensor component, an equation ?F1(ij) using ?1 is computed based on a function W(F) of an inputted tensor amount F and a value (F=F?) of F. For each (kl)-th tensor component, an equation ˜?F2(kl) using ?1 and ?2 is computed based on the value (F=F?) of F. For each combination of an (ij)-th and a (kl)-th component, a function W(F?+?F1(ij)+˜?F2(kl)) is computed using the computed equations ?F1(ij) and ˜?F2(kl). For each (ij)-th component, a coefficient of ?1 in the function W(F?+?F1(ij)+˜?F2(kl)) is removed, and stress, based on a first order derivative with respect to the amount F of the function W(F), is computed. For each combination of an (ij)-th and a (kl)-th component, a coefficient of ?1·?2 in the function W(F?+?F1(ij)+˜?F2(kl)) is removed, and a material Jacobian, based on a second order derivative with respect to the amount F of the function W(F), is computed.

Abstract: A warning means for a safety valve of a hydraulic power unit and a hydraulic power unit having the same for use in a lifting jack, a vehicle lift, or the like, are disclosed. When an overload is given to a cylinder chamber of a hydraulic power unit, a safety valve is automatically opened so as to release an oil in the overloaded cylinder chamber back to an oil tank. When the safety valve is opened, a warning means switches on a caution buzzer and a caution lamp to appeal the overload to the senses of eyesight and hearing of a human being in order to prevent an accident to be followed previously. The warning means comprises a reed switch and a magnet adapted to be moved by the oil passed through the safety valve.