My question is that there are many amaal in which a recitation or namaz is asked to offer for 40 days.How can a woman perform these amaal? It will be discontinued due to the menstrual cycle so how would it be possible for woman to complete 40 days?

She can start the amaals and if it is to do for 40 days, she can continue after her periods. For further reference please kindly refer to the Ahkaam book of your Marja Taqleed.