How does the structure of 'One Day in the Life of Ivan Denisovich' reflect its main concerns?

The novel portrays one day in the life of a prisoner who has been wrongly sentenced to a Soviet gulag for an infraction he did not commit. By focusing on just one day, from sunrise to sunset, Solzenitsyn is able to portray the way in which Shukhov, the protagonist, and his fellow inmates merely concentrate on survival. Their every moment is consecrated to survival of the harsh conditions and unending tedium of their lives.

Shukhov's failures, such as his inability to have the day off from work because he is sick, and his successes, such as earning some of Tsezar's package and having some kasha at dinner, are small and routine in nature. His life, in all its highs and lows, is concentrated on minute victories that enable him to survive. In so doing, he celebrates his victory over inhumanity and his ability to survive and find joy even in the midst of mind-numbing boredom and senseless brutality.

The structure of One Day in the Life of Ivan Denisovich, which follows a single day in the life of the prisoner, reflects the book's central concern with day-to-day survival. Ivan doesn't think past surviving one day at a time because the conditions he faces in a Soviet prison camp in Siberia are so severe. The weather is freezing cold. The work is brutally hard. Food is scarce. The other prisoners will steal from you or block the heat from the stove in their own quest to survive. Getting sick is a constant fear. There is very little to look forward to in this bleak world.

By focusing in a detached way on the details of a single typical day, the book captures the reality of what life is like in a labor camp. We see how almost every minute Denisovich faces a challenge to survival. We see how the smallest pleasures magnify in such a situation. For example, Denisovich welcomes his brutally hard labor because it warms him up in the subzero weather and makes the time pass more quickly.

By the end of the day, the reader is convinced that he or she would not want to spend even one day in such a place. Yet at the end of the day, ironically, Denisovich can feel happy that he has had many "strokes of luck" that day, such as enjoying building a wall, not getting sick, managing to buy some tobacco, and, most of all, surviving to face another day.

This novella was written by a Soviet during the Soviet reign in Russia.  After the Bolshevik revolution, the USSR came under the tyrannical leadership of Stalin, who persecuted, abused, and murdered many of his citizens.  While things improved during Kruschev's reign, much of the repression was still in place, including the work camps.

The concern in this short novel is to demonstrate the dehumanization of Russian citizens during this reign.  They are treated like animals, or more accurately, like the machinery of the state.  Their usefulness existed only in their ability to produce, and little was done to recognize them as individuals or treat them as humans.  Readers see this in the number identification tags of the work camp prisoners, who have been denied their right to a name.  Solzhenitsyn was seeking to expose the horrors that existed.

Instead of using emotional tactics, the author wrote in a more impersonal way.  He used the third person narrative instead of the first, and avoided needless words, particularly excessive description.  This echoes the lack of emotion and compassion with which the prisoners were treated.  In addition, Solzhenitsyn chooses to use the novella, and limit the story to one day.  More days,  more information, could easily distract the reader.  A shorter, more concise portrayal of facts is more powerful and convincing.

What notable aspects are there in the prose of 'One Day in the Life of Ivan Denisovich'?

This is a very broad question, and it's complicated by the fact that most of us are probably reading Solzhenitsyn in translation. Therefore the unique qualities of his Russian prose are inaccessible to us. Ideally, one would need to look at several different translations and compare them in order to gather with what style the original might be written. (Most of us obviously don't have the time to do this unless we are Solzhenitsyn specialists writing a doctoral thesis on him.) We also have to deal with the reality that it's difficult for any translator to convey the precise qualities of the original. In addition, different things about the prose will stand out for different readers. But the issue may not be as complicated as all of this suggests. A few basic conclusions can be drawn about Solzhenitsyn's prose without overthinking your question.

For me, the striking feature of his writing style is the matter-of-fact way in which it conveys the harsh details of life in the gulag. This quality reminds me of George Orwell's analysis of Arthur Koestler's writings, specifically, his analysis of Koestler's Darkness at Noon. Orwell is worth quoting at some length. He wrote this about Darkness at Noon:

The grown-upness, the lack of surprise or denunciation, the pity and irony with which the story is told, show the advantage, when one is handling a theme of this kind, of being a European. The book reaches the stature of tragedy, whereas an English or American writer could at most have made it into a polemical tract.

One might question Orwell's assertion about the inability of anglophone writers to deal with material of this nature, but his description of Koestler is insightful. Had Orwell lived to read One Day in the Life of Ivan Denisovich, he might have thought the same of Solzhenitsyn. Shukhov's day is described as if there is nothing abnormal about it. Obviously the experience of living in a Soviet prison camp is unimaginable by people who haven't been there or gone through something similar. But Solzhenitsyn narrates it in a dry, unsurprised manner. Here is the description of breakfast:

They sat in the cold mess hall, most of them eating with their hats on, eating slowly, picking out putrid little fish from under leaves of boiled black cabbage and spitting the bones out on the table. When the bones formed a heap and it was the turn of another squad, someone would sweep them off and they'd be trodden into a mush on the floor. It was considered bad manners to spit the fishbones straight out onto the floor. [translation by Ralph Parker]

This is actually a mild passage in the context of the entire story. It doesn't convey the physical brutality that is the worst part of prison life. Because Shukhov has already been in the camp for years, the "new normal" isn't at all new to him. It is precisely Shukhov's bored sense of his environment that Solzhenitsyn conveys to the reader. In all, the way the story is told makes it embody a universal truth: that people come to accept almost anything to survive.