I wonder if you are using the correct power supply, or is it broken and not supplying charge to your laptop. If the battery is too low then this can also cause the effect you are describing - even with the charger working correctly. Also the battery could be faulty.
My advice would be to try removing the battery and use only the charger to power the laptop.
If this works then the battery could be either too low and it is drawing all the current that the power supply can deliver, or the battery could be faulty. Try leaving the battery in and the laptop on charge for a few hours and see if it works then. If it does then the battery will have been too low.
Finally, if all this fails a new charger that is compatible with your laptop (correct voltage and power output) may be needed. see if you can borrow one before buying one in case it has more serious cause.
Please let me know how you get on.
I really appreciate thank you messages as a payment for solving issues :o)
i opened my laptop.
in motherboard two chip was crashed .
one that chip was mosfet and for other I can't find any datasheet(1 is tpc8065 and 2 maybe is ff b12).
now I want motherboard datasheet .( lenovo e531 ).
I think the problem with the shutting off your laptop could be related to malfunctioning of the cooling system, less thermic paste or incorrect currency going through the motherboard provided by the PSU. For example a resistor could be burnt and therefore not providing reducing of the current flow so my recommendation is to bring your laptop to a technician to make the tests of the motherboard.
I am beginning to agree with KY_WDs reply, but before you take it to a repair shop, what is the power output of your power supply? What output voltage does it have (usually about 19V) and what current can it supply (supplies in Amps (A)). You will usually find this information on a sticker on the powet supply.